Question 1

The weights of 6-week-old poults (juvenile turkeys) are normally distributed with a mean 9.1 pounds and standard deviation 2.4 pound(s). Find the 13th percentile of the weights.
A)7.67 lb
B)6.39 lb
C)7.03 lb
D)5.75 lb

Accepted Answer

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Question 2

The weights of 6-week-old poults (juvenile turkeys) are normally distributed with a mean 9.1 pounds and standard deviation 2.4 pounds. Find the first quartile of the weight.
A)8.24 lb
B)8.99 lb
C)6.74 lb
D)7.49 lb

Accepted Answer

The first quartile (Q1) corresponds to the 25th percentile of a normal distribution. Using the Z-score table, the Z-score for the 25th percentile is approximately -0.675. Using the formula: Q1 = mean + (Z * standard deviation), we get Q1 = 9.1 + (-0.675 * 2.4) = 7.49 pounds.

Question 3

Use the Central Limit Theorem to find the indicated probability. The sample size is  n , the population proportion is  $\hat { p }$ , and the sample proportion is
$n = 180 , p = 0.29 ; P ( \hat { p } < 0.34 )$
A)  0.9463 
B)  0.9525 
C)  0.9306 
D)  0.9474

Accepted Answer

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Question 4

The mean annual income for people in a certain city (in thousands of dollars) is 38, with a standard deviation of 31. A pollster draws a sample of 43 people to interview. Find the 68th percentile of the sample mean.
A)37.7 thousand dollars
B)38.7 thousand dollars
C)40.2 thousand dollars
D)42.3 thousand dollars

Accepted Answer

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Question 5

For a particular diamond mine,  76%  of the diamonds fail to qualify as "gemstone grade". A random sample of 96 diamonds is analysed. Find the mean 
A)  0.044 
B)  0.24 
C)  0.96 
D)  0.76

Accepted Answer

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Question 6

A bottler of drinking water fills plastic bottles with a mean volume of 994 milliliters(mL)and standard deviation 5 mL. The fill volumes are normally distributed. Whatproportion of bottles have volumes less than 995 mL?
A)0.5793
B)0.9974
C)0.5596
D)1.0000

Accepted Answer

To find the proportion of bottles with volumes less than 995 mL, we use the Z-score formula: Z = (X - μ) / σ, where X is the value of interest (995 mL), μ is the mean (994 mL), and σ is the standard deviation (5 mL). Calculating the Z-score gives Z = (995 - 994) / 5 = 0.2. Looking up 0.2 in a standard normal distribution table or using a calculator gives a proportion of approximately 0.5793.

Question 7

The mean annual income for people in a certain city (in thousands of dollars) is 40, with a standard deviation of 35. A pollster draws a sample of 48 people to interview. What is the probability that the sample mean income is between 34 and 45 (thousands of dollars)?
A)0.2781
B)0.1611
C)0.8389
D)0.7219

Accepted Answer

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Question 8

A sample of size 39 will be drawn from a population with mean 26 and standard deviation 14. Find the probability that $\bar { x }$ will be less than  29 . 
A)  0.8925 
B)  0.0901 
C)  0.9099 
D)  0.8770

Accepted Answer

The standard error is 14/sqrt(39). The z-score for $\bar{x} = 29$ is (29-26)/(14/sqrt(39)) ≈ 1.34. Using the standard normal distribution table, the probability of z < 1.34 is approximately 0.9099.

Question 9

A sample of size 70 will be drawn from a population with mean 24 and standard deviation 10. Find the probability that  $\bar { x }$  will be between 22 and 25 .
A)  0.7521 
B)  0.0475 
C)  0.7326 
D)  0.2005

Accepted Answer

The probability that $\bar{x}$ will be between 22 and 25 can be found using the Central Limit Theorem, which states that the sampling distribution of the sample mean will be normally distributed (or approximately so) if the sample size is large enough (n > 30 is a common rule of thumb), regardless of the shape of the population distribution. Given a population mean ($\mu$) of 24, a population standard deviation ($\sigma$) of 10, and a sample size (n) of 70, we can calculate the standard error of the mean ($\sigma_{\bar{x}}$) as $\sigma / \sqrt{n}$ = 10 / $\sqrt{70}$ ≈ 1.195. To find the probability that $\bar{x}$ is between 22 and 25, we convert these x values to z-scores using the formula $z = (\bar{x} - \mu) / \sigma_{\bar{x}}$. For $\bar{x} = 22$, $z = (22 - 24) / 1.195 ≈ -1.67$. For $\bar{x} = 25$, $z = (25 - 24) / 1.195 ≈ 0.84$.Using the standard normal distribution table or a calculator, we find the probabilities corresponding to these z-scores and subtract the smaller from the larger to find the probability that $\bar{x}$ falls between 22 and 25. This calculation yields a probability of approximately 0.7521, making option A the correct choice.

Question 10

Use the Central Limit Theorem to find the indicated probability. The sample size is  n , the population proportion is  $\hat { p }$ , and the sample proportion is
$n=117, p=0.83 ; P(0.79<\hat{p}<0.88)$

A)  0.0749 
B)  0.1251 
C)  0.9251 
D)  0.8000

Accepted Answer

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Question 11

A ferry will safely accommodate 66 tons of passenger cars. Assume that the mean weight of a passenger car is 1.7 tons with standard deviation 0.5 tons. If a random sample of 36 cars are loaded onto the ferry, what is the probability that the maximum safe weight will be exceeded?
A)0.0548
B)0.0668
C)0.9452
D)0.0384

Accepted Answer

The probability that the maximum safe weight will be exceeded is the probability that the sample mean weight of the 36 cars is greater than 66/36 = 1.83 tons. The sample mean weight is normally distributed with mean 1.7 tons and standard deviation 0.5/sqrt(36) = 0.0833 tons. The probability that the sample mean weight is greater than 1.83 tons is the area under the normal curve to the right of 1.83 tons, which is 0.0548.

Question 12

A bottler of drinking water fills plastic bottles with a mean volume of 993 milliliters(mL)and standard deviation 6 mL. The fill volumes are normally distributed. Whatproportion of bottles have volumes between 991 mL and 997 mL?
A)0.3779
B)0.7486
C)0.3707
D)0.3377

Accepted Answer

The proportion of bottles with volumes between 991 mL and 997 mL is the area under the normal distribution curve between these two values. Using a standard normal distribution table, we find that the area between z = -0.33 and z = 0.67 is 0.3779.

Question 13

A certain car model has a mean gas mileage of 29 miles per gallon (mpg) with a standard deviation 5 mpg. A pizza delivery company buys 38 of these cars. What is the probability that the average mileage of the fleet is greater than 27.8 mpg?
A)0.9535
B)0.9306
C)0.0465
D)0.8599

Accepted Answer

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Question 14

Use the Central Limit Theorem to find the indicated probability. The sample size is  n , the population proportion is  $\hat { p }$ , and the sample proportion is
$n = 160 , p = 0.29 ; P ( \hat { p } > 0.3 )$
A)  0.6103 
B)  0.3483 
C)  0.3300 
D)  0.3897

Accepted Answer

The Central Limit Theorem allows us to use the normal distribution to approximate the sampling distribution of the sample proportion. Calculate the standard error, then find the z-score for $\hat{p} = 0.3$, and use the standard normal distribution to find the probability.

Question 15

A sample of size 42 will be drawn from a population with mean 34 and standard deviation 8. Find the probability that $\bar { x }$ will be greater than 36 .
A)  0.0526 
B)  0.9474 
C)  0.0749 
D)  0.0351

Accepted Answer

To find the probability that $\bar{x}$ will be greater than 36, we use the Central Limit Theorem. The standard error (SE) of the sample mean is $\sigma/\sqrt{n} = 8/\sqrt{42}$. We calculate the z-score for $\bar{x} = 36$ as $z = (36 - 34) / (8/\sqrt{42})$. Using the z-score, we find the probability from the standard normal distribution table, which gives us approximately 0.0526.

Question 16

A sample of size 40 will be drawn from a population with mean 98 and standard deviation 24. Find the 21st percentile of  $\bar { x }$
A)  90.8 
B)  91.4 
C)  93.8 
D)  94.9

Accepted Answer

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Question 17

The mean number of pets per household is 3.25 with standard deviation 1.3. A sample of 59 households is drawn. Find the 74th percentile of the sample mean.
A)4.11
B)2.70
C)3.86
D)3.36

Accepted Answer

The 74th percentile of the sample mean can be found using the formula for the z-score: z = (X - μ) / (σ/√n). For the 74th percentile, the z-score is approximately 0.64. Using the given mean (μ = 3.25) and standard deviation (σ = 1.3), and sample size (n = 59), we calculate the sample mean X = μ + z*(σ/√n) = 3.25 + 0.64*(1.3/√59) ≈ 3.36.

Question 18

The weights of 6-week-old poults (juvenile turkeys) are normally distributed with a mean 8.6 pounds and standard deviation 1.9 pounds. A turkey farmer wants to provide a money-back guarantee that her 6-week poults will weigh at least a certain amount. What weight should she guarantee so that she will have to give her customer's money back only 1% of the time?
A)4.59 lb
B)3.34 lb
C)5.00 lb
D)4.17 lb

Accepted Answer

The z-score corresponding to a probability of 0.01 is -2.33. So, the weight that the farmer should guarantee is 8.6 - 2.33 * 1.9 = 4.17 pounds.

Question 19

The mean annual income for people in a certain city (in thousands of dollars) is 42, with a standard deviation of 38. A pollster draws a sample of 40 people to interview. What is the probability that the sample mean income is less than 35 (thousands of dollars)
A)0.8554
B)0.1210
C)0.1446
D)0.0934

Accepted Answer

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Question 20

A certain car model has a mean gas mileage of 31 miles per gallon (mpg) with a standard deviation 3 mpg. A pizza delivery company buys 35 of these cars. What is the probability that the average mileage of the fleet is between 30.9 and 31.2 mpg?
A)0.2310
B)0.6517
C)0.4207
D)0.7690

Accepted Answer

The correct answer is A.The central limit theorem states that the distribution of sample means will be approximately normal, regardless of the shape of the population distribution, as long as the sample size is large enough. In this case, the sample size is 35, which is large enough to apply the central limit theorem.The mean of the sample mean distribution will be equal to the population mean, which is 31 mpg. The standard deviation of the sample mean distribution will be equal to the population standard deviation divided by the square root of the sample size, which is 3 mpg / sqrt(35) = 0.548 mpg.Therefore, the probability that the average mileage of the fleet is between 30.9 and 31.2 mpg is equal to the probability that the sample mean is between 30.9 and 31.2 mpg. This probability can be calculated using the normal distribution with a mean of 31 mpg and a standard deviation of 0.548 mpg. Using a standard normal distribution table, we find that the probability is 0.2310.

Quiz 7: Confidence Intervals

The weights of 6-week-old poults (juvenile turkeys) are normally distributed with a mean 9.1 pounds and standard deviation 2.4 pound(s) . Find the 13th percentile of the weights.

The weights of 6-week-old poults (juvenile turkeys) are normally distributed with a mean 9.1 pounds and standard deviation 2.4 pounds. Find the first quartile of the weight.

Use the Central Limit Theorem to find the indicated probability. The sample size is n , the population proportion is $\hat { p }$ , and the sample proportion is $n = 180 , p = 0.29 ; P ( \hat { p } < 0.34 )$

The mean annual income for people in a certain city (in thousands of dollars) is 38, with a standard deviation of 31. A pollster draws a sample of 43 people to interview. Find the 68th percentile of the sample mean.

For a particular diamond mine, 76% of the diamonds fail to qualify as "gemstone grade". A random sample of 96 diamonds is analysed. Find the mean

A bottler of drinking water fills plastic bottles with a mean volume of 994 milliliters(mL) and standard deviation 5 mL. The fill volumes are normally distributed. Whatproportion of bottles have volumes less than 995 mL?

The mean annual income for people in a certain city (in thousands of dollars) is 40, with a standard deviation of 35. A pollster draws a sample of 48 people to interview. What is the probability that the sample mean income is between 34 and 45 (thousands of dollars) ?

A sample of size 39 will be drawn from a population with mean 26 and standard deviation 14. Find the probability that $\bar { x }$ will be less than 29 .

A sample of size 70 will be drawn from a population with mean 24 and standard deviation 10. Find the probability that $\bar { x }$ will be between 22 and 25 .

Use the Central Limit Theorem to find the indicated probability. The sample size is n , the population proportion is $\hat { p }$ , and the sample proportion is $n=117, p=0.83 ; P(0.79<\hat{p}<0.88)$

A ferry will safely accommodate 66 tons of passenger cars. Assume that the mean weight of a passenger car is 1.7 tons with standard deviation 0.5 tons. If a random sample of 36 cars are loaded onto the ferry, what is the probability that the maximum safe weight will be exceeded?

A bottler of drinking water fills plastic bottles with a mean volume of 993 milliliters(mL) and standard deviation 6 mL. The fill volumes are normally distributed. Whatproportion of bottles have volumes between 991 mL and 997 mL?

A certain car model has a mean gas mileage of 29 miles per gallon (mpg) with a standard deviation 5 mpg. A pizza delivery company buys 38 of these cars. What is the probability that the average mileage of the fleet is greater than 27.8 mpg?

Use the Central Limit Theorem to find the indicated probability. The sample size is n , the population proportion is $\hat { p }$ , and the sample proportion is $n = 160 , p = 0.29 ; P ( \hat { p } > 0.3 )$

A sample of size 42 will be drawn from a population with mean 34 and standard deviation 8. Find the probability that $\bar { x }$ will be greater than 36 .

A sample of size 40 will be drawn from a population with mean 98 and standard deviation 24. Find the 21st percentile of $\bar { x }$

The mean number of pets per household is 3.25 with standard deviation 1.3. A sample of 59 households is drawn. Find the 74th percentile of the sample mean.

The mean annual income for people in a certain city (in thousands of dollars) is 42, with a standard deviation of 38. A pollster draws a sample of 40 people to interview. What is the probability that the sample mean income is less than 35 (thousands of dollars)

A certain car model has a mean gas mileage of 31 miles per gallon (mpg) with a standard deviation 3 mpg. A pizza delivery company buys 35 of these cars. What is the probability that the average mileage of the fleet is between 30.9 and 31.2 mpg?

Quiz 7: Confidence Intervals

The weights of 6-week-old poults (juvenile turkeys) are normally distributed with a mean 9.1 pounds and standard deviation 2.4 pound(s) . Find the 13th percentile of the weights.

The weights of 6-week-old poults (juvenile turkeys) are normally distributed with a mean 9.1 pounds and standard deviation 2.4 pounds. Find the first quartile of the weight.

Use the Central Limit Theorem to find the indicated probability. The sample size is n , the population proportion is p^\hat { p }p^​ , and the sample proportion is n=180,p=0.29;P(p^<0.34) n = 180 , p = 0.29 ; P ( \hat { p } < 0.34 ) n=180,p=0.29;P(p^​<0.34)

The mean annual income for people in a certain city (in thousands of dollars) is 38, with a standard deviation of 31. A pollster draws a sample of 43 people to interview. Find the 68th percentile of the sample mean.

For a particular diamond mine, 76% of the diamonds fail to qualify as "gemstone grade". A random sample of 96 diamonds is analysed. Find the mean

A bottler of drinking water fills plastic bottles with a mean volume of 994 milliliters(mL) and standard deviation 5 mL. The fill volumes are normally distributed. Whatproportion of bottles have volumes less than 995 mL?

The mean annual income for people in a certain city (in thousands of dollars) is 40, with a standard deviation of 35. A pollster draws a sample of 48 people to interview. What is the probability that the sample mean income is between 34 and 45 (thousands of dollars) ?

A sample of size 39 will be drawn from a population with mean 26 and standard deviation 14. Find the probability that xˉ\bar { x }xˉ will be less than 29 .

A sample of size 70 will be drawn from a population with mean 24 and standard deviation 10. Find the probability that xˉ\bar { x }xˉ will be between 22 and 25 .

Use the Central Limit Theorem to find the indicated probability. The sample size is n , the population proportion is p^\hat { p }p^​ , and the sample proportion is n=117,p=0.83;P(0.79<p^<0.88) n=117, p=0.83 ; P(0.79<\hat{p}<0.88) n=117,p=0.83;P(0.79<p^​<0.88)

A ferry will safely accommodate 66 tons of passenger cars. Assume that the mean weight of a passenger car is 1.7 tons with standard deviation 0.5 tons. If a random sample of 36 cars are loaded onto the ferry, what is the probability that the maximum safe weight will be exceeded?

A bottler of drinking water fills plastic bottles with a mean volume of 993 milliliters(mL) and standard deviation 6 mL. The fill volumes are normally distributed. Whatproportion of bottles have volumes between 991 mL and 997 mL?

A certain car model has a mean gas mileage of 29 miles per gallon (mpg) with a standard deviation 5 mpg. A pizza delivery company buys 38 of these cars. What is the probability that the average mileage of the fleet is greater than 27.8 mpg?

Use the Central Limit Theorem to find the indicated probability. The sample size is n , the population proportion is p^\hat { p }p^​ , and the sample proportion is n=160,p=0.29;P(p^>0.3) n = 160 , p = 0.29 ; P ( \hat { p } > 0.3 ) n=160,p=0.29;P(p^​>0.3)

A sample of size 42 will be drawn from a population with mean 34 and standard deviation 8. Find the probability that xˉ\bar { x }xˉ will be greater than 36 .

A sample of size 40 will be drawn from a population with mean 98 and standard deviation 24. Find the 21st percentile of xˉ\bar { x }xˉ

The mean number of pets per household is 3.25 with standard deviation 1.3. A sample of 59 households is drawn. Find the 74th percentile of the sample mean.

The mean annual income for people in a certain city (in thousands of dollars) is 42, with a standard deviation of 38. A pollster draws a sample of 40 people to interview. What is the probability that the sample mean income is less than 35 (thousands of dollars)

A certain car model has a mean gas mileage of 31 miles per gallon (mpg) with a standard deviation 3 mpg. A pizza delivery company buys 35 of these cars. What is the probability that the average mileage of the fleet is between 30.9 and 31.2 mpg?

Use the Central Limit Theorem to find the indicated probability. The sample size is n , the population proportion is $\hat { p }$ , and the sample proportion is $n = 180 , p = 0.29 ; P ( \hat { p } < 0.34 )$

A sample of size 39 will be drawn from a population with mean 26 and standard deviation 14. Find the probability that $\bar { x }$ will be less than 29 .

A sample of size 70 will be drawn from a population with mean 24 and standard deviation 10. Find the probability that $\bar { x }$ will be between 22 and 25 .

Use the Central Limit Theorem to find the indicated probability. The sample size is n , the population proportion is $\hat { p }$ , and the sample proportion is $n=117, p=0.83 ; P(0.79<\hat{p}<0.88)$

Use the Central Limit Theorem to find the indicated probability. The sample size is n , the population proportion is $\hat { p }$ , and the sample proportion is $n = 160 , p = 0.29 ; P ( \hat { p } > 0.3 )$

A sample of size 42 will be drawn from a population with mean 34 and standard deviation 8. Find the probability that $\bar { x }$ will be greater than 36 .

A sample of size 40 will be drawn from a population with mean 98 and standard deviation 24. Find the 21st percentile of $\bar { x }$