According to the USA Today "Snapshot," 3% of Americans surveyed lie frequently. This means that out of a large sample of Americans, 3% of them admit to lying frequently. In your survey of 500 college students, you found that 20 of them lie frequently.
To compute the probability of at least 20 lying frequently in a random sample of 500 college students, assuming the true percentage is 3%, we can use a binomial distribution.
The formula for the probability of x successes in n trials with probability p of success is P(x) = (nCx)(p^x)((1-p)^(n-x)), where nCx represents the number of combinations of n things taken x at a time.
Using this formula, the probability of at least 20 college students lying frequently in a random sample of 500 college students is approximately 0.00002, or 0.002%. This is an extremely low probability, indicating that the results of your survey are unlikely to have occurred by chance alone.
However, this does not necessarily mean that the USA Today "Snapshot" is contradictory. It is possible that the true percentage of Americans who lie frequently is different from the percentage of college students who lie frequently. Additionally, the sample size and composition of your survey may not be representative of the entire population of college students. Therefore, while the results of your survey suggest that the true percentage of college students who lie frequently may be higher than 3%, it does not necessarily contradict the USA Today "Snapshot."
According to a USA Today "Snapshot," 3% of Americans surveyed lie frequently. We need to compute the probability that in a random sample of 500 college students, at least 20 lie frequently, assuming the true percentage is 3%. To do this, we can use the binomial probability formula:
P(x >= 20) = 1 - P(x <= 19)
Here, n = 500 (sample size), p = 0.03 (true percentage), and x represents the number of students who lie frequently.
Step 1:
Calculate the cumulative probability P(x <= 19):
We can use a cumulative binomial probability table or a calculator with a binomial cumulative distribution function (CDF). Using the CDF, we get:
P(x <= 19) = binomcdf(500, 0.03, 19) ≈ 0.964
Step 2:
Calculate the probability P(x >= 20):
P(x >= 20) = 1 - P(x <= 19) = 1 - 0.964 = 0.036
The probability that at least 20 out of 500 college students lie frequently is 0.036 or 3.6%. This result is slightly higher than the USA Today Snapshot's 3% figure.
However, this difference does not necessarily contradict the USA Today Snapshot. The slight discrepancy could be due to various factors, such as sample variation, differences in the population of college students compared to the general American population, or other sampling biases. The probability we calculated (3.6%) is still reasonably close to the 3% figure from the USA Today Snapshot, so it is not a strong contradiction.
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Help WILL GIVE BRAINLIEST HEELLPPO
Answer:
B: 4.5
Step-by-step explanation:
Need help quick please!!!
Answer:
b = 12 Km
Step-by-step explanation:
using Pythagoras' identity in the right triangle
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is
b² + 16² = 20²
b² + 256 = 400 ( subtract 256 from both sides )
b² = 144 ( take square root of both sides )
b = [tex]\sqrt{144}[/tex] = 12
Find the smallest number n of terms needed to obtain an approximation of the series IM8 12ke 0.49k2 accurate to 10-6. k=1 n=
The smallest value of n that satisfies this inequality is n = 11. Therefore, we need at least 11 terms to obtain an approximation of the series IM8 12ke 0.49k2 accurate to 10-6.
To find the smallest number of terms needed to obtain an approximation of the series IM8 12ke 0.49k2 accurate to 10-6, we need to use the formula for the partial sum of a series. The partial sum of the given series up to n terms is:
S(n) = IM8 + 12e + 0.49(2^2) + 0.49(3^2) + ... + 0.49(n^2)
We want to find the smallest value of n such that the error between S(n) and the true value of the series is less than 10^-6. The error between S(n) and the true value of the series can be approximated by the absolute value of the next term in the series:
|an+1| = 0.49((n+1)^2)
So we need to find the smallest value of n such that:
|an+1| < 10^-6
0.49((n+1)^2) < 10^-6
(n+1)^2 < (10^-6)/0.49
n+1 < sqrt((10^-6)/0.49)
n < sqrt((10^-6)/0.49) - 1
n < 11.75
Since n must be a whole number, the smallest value of n that satisfies this inequality is n = 11. Therefore, we need at least 11 terms to obtain an approximation of the series IM8 12ke 0.49k2 accurate to 10-6.
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Assume the characteristic polynomial of a matrix A is det(A –λ I) = (1 - λ)2(5 –λ ). If possible give concrete examples of such a matrix so that: (a) A is diagonalizable but not diagonal; (b) A is not diagonalizable if not possible wxplain why
a) A is not diagonal because it is not possible to find a matrix P such that A = PDP^-1, where D is a diagonal matrix.
b) A is not diagonalizable.
(a) A is diagonalizable but not diagonal: One possible example of such a matrix A would be:
A = [[1, 1], [0, 5]]
The characteristic polynomial of A is det(A –λ I) = (1 - λ)2(5 –λ), as given. The eigenvalues of A are λ1 = 1 and λ2 = 5, both of which have algebraic multiplicity 2. The eigenvectors corresponding to λ1 = 1 are [1, 0] and [1, 1], while the eigenvector corresponding to λ2 = 5 is [0, 1]. It can be verified that the eigenvectors are linearly independent and thus form a basis for R2. Therefore, A is diagonalizable.
However, A is not diagonal because it is not possible to find a matrix P such that A = PDP^-1, where D is a diagonal matrix.
(b) A is not diagonalizable: One possible example of such a matrix A would be:
A = [[1, 1], [0, 1]]
The characteristic polynomial of A is det(A –λ I) = (1 - λ)^2, which has a repeated eigenvalue of λ = 1. The eigenvectors corresponding to λ = 1 are [1, 0] and [0, 1], but they do not form a basis for R2 because they are linearly dependent. Therefore, A is not diagonalizable.
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When the population standard deviation is known, the confidence interval for the population mean is based on the:Chi-square statistict-statisticz-statisticF-statistic
When the population standard deviation is known, the confidence interval for the population mean is based on the z-statistic.
When the population standard deviation is known, the confidence interval for the population mean is based on the z-statistic.
The formula for the confidence interval for the population mean when the population standard deviation is known is given by:
CI = X ± z(α/2) * σ/√n
Where:
X is the sample mean
σ is the population standard deviation
n is the sample size
z(α/2) is the z-score corresponding to the desired level of confidence (e.g. for a 95% confidence interval, α = 0.05 and z(α/2) = 1.96)
The z-statistic is used in this formula to determine the width of the confidence interval. It is based on the standard normal distribution and represents the number of standard deviations the sample mean is from the population mean. The z-score is calculated using the formula:
z = (X - μ) / (σ/√n)
Where μ is the population mean.
The z-score is used to find the critical values for the confidence interval, which are obtained by multiplying it by the standard error of the mean (σ/√n). These critical values define the endpoints of the confidence interval.
In summary, when the population standard deviation is known, the confidence interval for the population mean is based on the z-statistic, which is used to calculate the critical values for the confidence interval.
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What is the greatest value in the data set
Answer:
Step-by-step explanation:
Maximum :)
Suppose follows the standard normal distribution. Use the calculator provided, or that, to determine the value of c so that the following true P(2>c) 0.2643 Round your answer to two decimal places 0 X
The z-score for 0.7129 is approximately 0.55. The value of c is 0.55, rounded to two decimal places.
1. We're given P(2 > c) = 0.2643, which means the area under the standard normal distribution curve between 2 and c is 0.2643.
2. We'll use the z-table or a calculator with a standard normal distribution function to find the corresponding z-score for c.
3. To find the area to the left of c, we need to first find the area to the left of 2. The z-score for 2 is 0.9772 (from the z-table or using a calculator).
4. Now, subtract the given area (0.2643) from the area to the left of 2: 0.9772 - 0.2643 = 0.7129.
5. Look up the z-score corresponding to the area 0.7129 in the z-table, or use a calculator with the inverse standard normal distribution function. The z-score for 0.7129 is approximately 0.55.
6. Therefore, the value of c is 0.55, rounded to two decimal places.
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Assume z is a standard normal random variable. What is the value of z if the area to the right of zis 9803? 0 -2.06 4803 0.0997 3.06
The value of z, In the above statistics-based question where the area to the right of z is 0.9803, is approximately 1.81.
In statistics, the standard normal distribution is a specific distribution of normal random variables with a mean of 0 and a standard deviation of 1. The area under the curve of a standard normal distribution is equal to 1, and the distribution is symmetric around the mean of 0.
To find the value of z for a given area to the right of z, we can use a standard normal distribution table or calculator. For example, using a standard normal distribution table, we can find the value of z that corresponds to an area of 0.0197 to the left of z. This value is approximately -1.81. Since the area to the right of z is 0.9803, we can find the value of z by subtracting -1.81 from 0, which gives us approximately 1.81.
Alternatively, we can use the inverse normal distribution function in Excel or another statistical software package to find the value of z directly. For example, the Excel function NORMSINV(0.9803) returns a value of approximately 1.81, which is the same as the value we obtained using the standard normal distribution table.
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Solve the inequality 3y<6
Answer:
Solving the inequality for y in 37<7 would be
y<2
BC¯¯¯¯¯¯¯¯ ∥ AD¯¯¯¯¯¯¯¯
What type of angle pairs are form with the 75∘
angle and ∠2?
vertical angles
corresponding angles
adjacent angles
alternate interior angles
The angles 75° and ∠2 are alternate interior angles.
Option D is the correct answer.
We have,
From the figure,
55°, ∠3, and 75° forms a straight angle.
Alternate angles are pairs of angles formed when a transversal line intersects two parallel lines.
Alternate angles are equal in measure, which means they have the same angle degree value.
So,
75° and ∠2 are alternate angles.
Thus,
75° and ∠2 are alternate angles.
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Un televisor costaba $1250 y al comprarlo nos han hecho un 20% de descuento ¿cuánto nos han descontado?
They discount you $250 from the television cost.
How to calculate how much did they discount?Discount is defined as a deduction from the usual cost of something.
Since the television cost $1250 and when you bought it they gave you a 20% discount. We can say:
discount = 20% of $1250
discount = 20/100 * $1250
discount = $250
Therefore, they discount you $250
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Question in English
A television cost $1250 and when we bought it they gave us a 20% discount. How much did they discount us?
Mike works a total of 59 hr per week at his two jobs. He makes $6 per hour at job A and $7 per hour at job B. If his total pay for one week is $374 before taxes, then how many hours does he work at each job?
Mike works 39 hours per week at Job A and 20 hours per week at Job B.
Calculating the work-rate of MikeWe need to formulate some expressions here.
Let:
Hours Mike works at Job A = x
Hours Mike works at Job B = y
We know that:
x + y = 59 ---------- equation 1
We also know that he makes $6 per hour at Job A, and $7 per hour at Job B, and his total pay is $374. So we can set up another equation based on his total pay:
6x + 7y = 374 --------- equation 2
Now we have two equations with two unknowns, which we can solve simultaneously.
Using substitution method:
solve for x in terms of y:
x = 59 - y
We can substitute this expression for x into equation 2:
6(59 - y) + 7y = 374
Simplifying and solving for y:
354 - 6y + 7y = 374
y = 20
So Mike works 20 hours per week at Job B. We can substitute this value for y into equation 1 to find x:
x + 20 = 59
x = 39
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The circle below has center C, and its radius is 7 yd. Given that mZDCE = 100°, find the length of the major arc DFE. Give an exact answer in terms of , and be sure to include the correct unit in your answer. F 100 Length of major arc DFE: D/O 8 JT yd yd² X yd³
The length of the major arc DFE is 10.11 π ft.
Given that, a circle C, with central angle 100°, and radius 7 yards,
We need to find the length of the major arc DFE,
The length of an arc = central angle / 360° × circumference
The central angle for the arc DFE = 360° - 100° = 260°
So, the length = 260° / 360° × π × 14
= 10.11 π ft
Hence, the length of the major arc DFE is 10.11 π ft.
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Which expressions will help you find the surface area of this net? Select all that apply.
The expression that will help in finding the surface area of the net are
9 x 51/2 x 4 x 6What is surface area?The external surface area of three-dimensional objects is referred to as the surface area, and is generally calculated in square units.
Calculating the surface area of certain 3D shapes requires one to use different formulas. depending on the shapes
The shapes encountered here are
rectangle = 9 x 5triangle = 1/2 x 4 x 6:earn more about surface area at
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use the method of your choice to determine the following probability. drawing three sevens in a row from a standard deck of cards when the drawn card is not returned to the deck each time. The probability of drawing three sevens is ______.
The probability of drawing three sevens in a row from a standard deck of cards when the drawn card is not returned to the deck each time is approximately 0.00012, or 0.012%.
To determine the probability of drawing three sevens in a row from a standard deck of cards without replacement, we can use the following method:
Step 1: Identify the total number of cards in a standard deck. A standard deck has 52 cards (13 ranks and 4 suits).
Step 2: Determine the number of sevens in the deck. There are 4 sevens (one from each suit).
The probability of drawing a seven from a standard deck of 52 cards is 4/52 or 1/13, since there are four sevens in the deck. After the first seven is drawn, there are 51 cards left in the deck, of which three are sevens. So the probability of drawing a second seven is 3/51. Similarly, after the second seven is drawn, there are 50 cards left in the deck, of which two are sevens. So the probability of drawing a third seven is 2/50.
Step 3: Calculate the probability of drawing the first seven. This would be the number of sevens divided by the total number of cards:
P(1st Seven) = 4/52
Step 4: After drawing the first seven, there are now 51 cards left in the deck and only 3 sevens remaining. Calculate the probability of drawing the second seven:
P(2nd Seven) = 3/51
Step 5: After drawing the second seven, there are now 50 cards left in the deck and only 2 sevens remaining. Calculate the probability of drawing the third seven:
P(3rd Seven) = 2/50
Step 6: To find the probability of all three events happening in a row, multiply the individual probabilities:
P(Three Sevens) = P(1st Seven) * P(2nd Seven) * P(3rd Seven) = (4/52) * (3/51) * (2/50)
Step 7: Calculate the result:
P(Three Sevens) = (4/52) * (3/51) * (2/50) = 0.0012 (approximately)
The probability of drawing three sevens in a row from a standard deck of cards without replacement is approximately 0.0012, or 0.12%.
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Why is the straightedge of a ruler not the same as a line?
Since a straightedge lacks measurement gradients, it can only be used to create or draw straight lines—not to measure length.
An instrument for drawing straight lines or ensuring their straightness is a straightedge or straight edge. It is typically referred to as a ruler if its length is marked with uniformly spaced markings. If no markings are present, it is just a straight edge.
Straight lines can be measured and marked with a ruler. A straight edge won't help you measure, but since they are typically more robustly constructed than rulers, they are a better tool for drawing straight lines. Most of the time, rulers can be used as a straight edge.
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The probability that X is a 2, 11, or 12 is:
a.) 1/36
b.) 2/36
c.) 3/36
d.) 4/36
Answer:
The correct answer is c.) 3/36.There are three favorable outcomes (2, 11, and 12) out of a total of 36 possible outcomes (assuming a fair six-sided number cube). Therefore, the probability of X being a 2, 11, or 12 is 3/36, which can be simplified to 1/12.
Step-by-step explanation:
QUESTION 1 of 10: A manufacturer buys a new machine that costs $50,000. The estimated useful life for the machine is ten years. The
machine can produce 1,000 units per month. If the machine ran at its capacity for ten years, what would be the fixed cost per unit based on
the cost of the machine per part manufactured? (Round to the nearest penny)
a) $. 42 / unit
ООО
b) $1. 00/unit
c) S4,167 / unit
d) $5. 000/unit
The fixed cost per unit based on cost of the machine per part manufactured is $0.42 per unit. Option ( A )
What is multiplication ?Multiplication is a mathematical operation that involves finding the product of two or more numbers or quantities. It is a way of adding a number to itself multiple times. The symbol used to represent multiplication is an "x" or a dot "·". For example, in the expression 5 x 6 = 30, 5 and 6 are multiplied together to give the product of 30. Multiplication can also be represented using parentheses, such as (5)(6) = 30. In addition, multiplication can be done with decimals, fractions, variables, and matrices.
To find the fixed cost per unit based on the cost of the machine per part manufactured, we need to calculate the total number of units produced by the machine over its estimated useful life, and then divide the cost of the machine by that number.
The machine runs at its capacity of 1,000 units per month for 10 years, so the total number of units produced by the machine is:
10 years x 12 months/year x 1,000 units/month = 120,000 units
The cost of the machine is $50,000, so the fixed cost per unit based on the cost of the machine per part manufactured is:
$50,000 ÷ 120,000 units = $0.4167 per unit
Rounding this to the nearest penny gives us the final answer of:
$0.42 per unit (option a)
Therefore, the fixed cost per unit based on cost of the machine per part manufactured is $0.42 per unit.
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A. When José is done, they always fill the gas tank.
B. When Liam is done, they always fill the gas tank.
C. When they're done, José always fills the gas tank.
D. When he's done, he always fills the gas tank.
Answer:
C. When they're done, José always fills the gas tank.
Help me please and thank you
Answer:
2700
Step-by-step explanation:
im pretty sure that volume is length times width times height so
if u times these 3 numbers together its 2700
At the burger palace, 2 hamburgers and 1 small order of fires cost 6. 9
The cost of one small order of fries at the Burger Palace is $1.09. The correct answer is not given in any option.
The price is another name for the cost of a thing from the perspective of a consumer. This is the price the seller sets for a product, which takes into account both the cost of manufacture and the markup the seller adds to increase profits.
Let's say a hamburger costs x dollars and a small order of French fries costs y dollars.
x--------> the cost of one hamburger
y--------> the cost one small order fries
we know that
2x+y=6.50
5x+5y=17.75
using a graph tool
see the attached figure
the solution is
x=2.5
y=1.09
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The complete question is
At The Burger Palace, 2 hamburgers and 1 small order of fries costs $6.50. The Clarke family ordered 5 hamburgers and 5 small orders of fries and paid $17.75.
Select the TWO equations that fit the scenario described above.
A) 2x+y=6.50
B) 6.50x+17.75y=5
C) 2x+5y=24.25
D) 5x+5y=6.50
E) 5x+5y=17.75
10
TIME REMA
59:4
What is the difference between marginal cost and marginal revenue?
O Marginal cost is the money earned from selling one more unit of a good. Marginal revenue is the money paid f
producing one more unit of a good.
Marginal cost is the money paid for producing one more unit of a good. Marginal revenue is the money earned
from selling one more unit of a good.
Marginal cost is the money a producer might make from one more unit. Marginal revenue is the money a produ
actually makes from one more unit.
O Marginal cost is the money a producer actually makes from one more unit. Marginal revenue is the money a
producer might make from one more unit.
The difference is: Marginal cost is the money paid for producing one more unit of a good. Marginal revenue is the money earned from selling one more unit of a good.
What is Marginal cost and Marginal revenue?Marginal cost (MC) is the additional outlay expended by a producer when they fabricate and supply one supplementary unit of an item or service. It symbolizes the replace in total costs caused by producing one extra piece.
Marginal revenue (MR), on the other hand, is the supplementary turnover generated when an establishment deals one more piece of a good or service. It signifies the transformation in complete revenue attained from selling an supplemental product.
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In government data, a household consists of all occupants of a dwelling unit. Choose an American household at random and count the number of people it contains. Here is the assignment of probabilities for the outcome. (The probability of finding 3 people in a household is the same as the probability of finding 4 people.) What probability should replace "?" in the table? Remember: there is a larger version of the charts on my website!answer choicesa. 0.04b. 0.09c. 0.32d. 0.16
Based on the information given, we know that the probability of finding 3 people in a household is the same as the probability of finding 4 people. Therefore, the probability that a randomly chosen American household contains 2 or 5 people is 1/6.
To determine the probability that should replace "?" in the table, we first need to recognize that the sum of probabilities for all possible outcomes must equal 1. Given that the probability of finding 3 people in a household is the same as the probability of finding 4 people, let's denote that probability as x.
Since the "?" represents the remaining probability, we can set up an equation:
x + x + ? = 1
The sum of the probabilities for all possible outcomes must equal 1. We know that there are 4 possible outcomes (households with 2, 3, 4, or 5 people).
Simplifying the equation:
3x + ? = 1
Since we know that the probability of finding 3 people in a household is the same as the probability of finding 4 people, we can set up another equation:
Now, let's plug in the answer choices and see which one gives us a valid probability distribution:
a) 0.04:
2x + 0.04 = 1
2x = 0.96
x = 0.48 (Invalid, since x should be the probability for finding 3 or 4 people and it's greater than the maximum probability value of 1)
b) 0.09:
2x + 0.09 = 1
2x = 0.91
x = 0.455 (Invalid for the same reason as options a)
c) 0.32:
2x + 0.32 = 1
2x = 0.68
x = 0.34 (Valid, as it falls within the probability range of 0 to 1)
d) 0.16:
2x + 0.16 = 1
2x = 0.84
x = 0.42 (Invalid for the same reason as options a)
Based on the calculations, option c (0.32) should replace "?" in the table, as it creates a valid probability distribution with the given conditions.
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pls help <333 (don’t mind the white part, it was wrong)
The length of MS is 10 cm and diameter of the circle is RS
Given that the midpoint of PQ is M
RM is 10 cm and PQ is 24 cm
We have to find the length of MS
As M is midpoint then RM=MS
MS = 10 cm
Now the diameter of the circle is RS because it passes through middle of the circle which is center O
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Which of the following equations has infinitely many solutions?
A
2x + 3 = 5 + 2x
B
2x + 3 = 5 + 3x
C
3x - 5 = -5 + 3x
D
2x - 5 = -5 + 3x
A. 2x + 3 = 5 + 2x has infinitely many solutions because the variable terms cancel out, leaving the statement 3 = 3, which is always true, regardless of the value of x.
please help sorry if its a lot
The values in the expression will be:
a. 4x
b. -4x
c. -16x
d. 4x + 5
e. 4x
f. 5x
g. 10 - 6x
h. 2x - 10
How to explain the expressionIt is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.
Based on the information, it should be noted that:
10x - 6x
= 4x
6x - 4x
= 2x
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The defect length of a corrosion defect in a pressurized steel pipe is normally distributed with mean value 28 mm and standard deviation 7.9 mm. in USE SALT (a) What is the probability that defect length is at most 20 mm? Less than 20 mm? (Round your answers to four decimal places.) at most 20mm _____
less than 20mm _____
(b) What is the 75th percentile of the defect length distribution-that is, the value that separates the smallest 75% of all lengths from the largest 25%? (Round your answer to four decimal places.)
______ mm (c) What is the 15th percentile of the defect length distribution? (Round your answer to four decimal places.) _____mm (d) What values separate the middle 80% of the defect length distribution from the smallest 10% and the largest 10%? (Round your answers to four decimal places.) smallest 10%_____ mm largest 10%______ mm
A) The same z-score and find the area to the left of it, which is 0.1562.
b) The 75th percentile of the defect length distribution is 33.32 mm.
C) The 15th percentile of the defect length distribution is 19.21 mm.
d)The values that separate the middle 80% of the defect length distribution from the smallest 10% and the largest 10% are 17.95 mm and 38.05 mm, respectively.
(a) To find the probability that the defect length is at most 20 mm, we need to calculate the z-score first:
z = (20 - 28) / 7.9 = -1.0127
Using a standard normal table or a calculator, we can find that the probability of a z-score less than or equal to -1.0127 is 0.1562. Therefore, the probability that the defect length is at most 20 mm is 0.1562.
To find the probability that the defect length is less than 20 mm, we can use the same z-score and find the area to the left of it, which is 0.1562.
(b) To find the 75th percentile of the defect length distribution, we need to find the z-score that corresponds to the area of 0.75 in the standard normal distribution. Using a standard normal table or a calculator, we can find that this z-score is approximately 0.6745.
Then, we can solve for the defect length:
z = (x - 28) / 7.9
0.6745 = (x - 28) / 7.9
x - 28 = 0.6745 * 7.9
x = 33.32
Therefore, the 75th percentile of the defect length distribution is 33.32 mm.
(c) To find the 15th percentile of the defect length distribution, we need to find the z-score that corresponds to the area of 0.15 in the standard normal distribution. Using a standard normal table or a calculator, we can find that this z-score is approximately -1.0364.
Then, we can solve for the defect length:
z = (x - 28) / 7.9
-1.0364 = (x - 28) / 7.9
x - 28 = -1.0364 * 7.9
x = 19.21
Therefore, the 15th percentile of the defect length distribution is 19.21 mm.
(d) To find the values that separate the middle 80% of the defect length distribution from the smallest 10% and the largest 10%, we need to find the z-scores that correspond to the areas of 0.1 and 0.9 in the standard normal distribution. Using a standard normal table or a calculator, we can find that these z-scores are approximately -1.2816 and 1.2816, respectively.
Then, we can solve for the defect lengths:
z = (x - 28) / 7.9
-1.2816 = (x - 28) / 7.9
x - 28 = -1.2816 * 7.9
x = 17.95
z = (x - 28) / 7.9
1.2816 = (x - 28) / 7.9
x - 28 = 1.2816 * 7.9
x = 38.05
Therefore, the values that separate the middle 80% of the defect length distribution from the smallest 10% and the largest 10% are 17.95 mm and 38.05 mm, respectively.
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0.32 + /100 = 0.54 + 32/100
Answer:
54
Step-by-step explanation:
0.32 + /100 = 0.54 + 32/100
0.32 + x/100 = 0.54 + 0.32
x / 100 = 0.54
x = 54
So, the answer is 54
consider the results of a poll where 48% of 331 americans who decide to not go to college do so because they cannot afford it. calculate a 90% confidence interval for the proportion of americans who decide to not go to college because they cannot afford it.
The 90% confidence interval for the proportion of Americans who decide not to go to college because they cannot afford it can be calculated using a statistical formula. The formula for a confidence interval is: CI = p ± zsqrt((p(1-p))/n)
Where CI is the confidence interval, p is the proportion of interest (in this case, 0.48 or 48%), and z is the critical value from the standard normal distribution for the desired level of confidence (in this case, 1.645 for 90% confidence), sqrt is the square root function, and n is the sample size (in this case, 331).
Plugging in the values, we get:
CI = 0.48 ± 1.645sqrt((0.48(1-0.48))/331)
CI = 0.48 ± 0.062
Thus, the 90% confidence interval for the proportion of Americans who decide not to go to college because they cannot afford it is (0.418, 0.542). This means that we can be 90% confident that the true proportion of Americans who decide not to go to college because they cannot afford it falls between 41.8% and 54.2%.
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The weekly sales of Honolulu Red Oranges is given by
q = 1040 - 20р.
Calculate the price elasticity of demand when the price is $32 per orange
The price elasticity of demand when the price is $32 per orange is 2
To calculate the price elasticity of demand, we need to use the formula:
E = (%Δq / %Δp) x (p/q)
where E is the price elasticity of demand, %Δq is the percentage change in quantity demanded, %Δp is the percentage change in price, and p/q is the average price-quantity ratio.
Given that the weekly sales of Honolulu Red Oranges is given by q = 1040 - 20p, we can find the derivative of q with respect to p as follows:
dq/dp = -20
This tells us that for every $1 increase in price, the quantity demanded will decrease by 20 units.
At a price of $32 per orange, the quantity demanded is:
q = 1040 - 20(32) = 424
If the price were to increase to $33 per orange, the new quantity demanded would be:
q' = 1040 - 20(33) = 404
Using these values, we can calculate the percentage changes in price and quantity demanded as:
%Δp = [(33 - 32) / 32] x 100% = 3.125%
%Δq = [(404 - 424) / 424] x 100% = -4.72%
The average price-quantity ratio is:
(p+ p')/2q = [(32 + 33)/2]/424 = 0.015
Now we can calculate the price elasticity of demand as:
E = (%Δq / %Δp) x (p/q) = (-4.72 / 3.125) x 0.015 = -0.023
Since the price elasticity of demand is negative, we know that Honolulu Red Oranges have an inelastic demand at a price of $32 per orange. This means that a 1% increase in price will lead to a less than 1% decrease in quantity demanded.
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