Question 1

Pinky Bauer, Chief Financial Officer of Harrison Haulers, Inc., suspects irregularities in the payroll system.If 10% of the 5,000 payroll vouchers issued since January 1, 2018, have irregularities, the probability that Pinky's random sample of 200 vouchers will have a sample proportion of between .06 and .14 is closest to ___________.

Accepted Answer

The answer of Pinky Bauer, Chief Financial Officer of Harrison...

Question 2

Catherine Chao, Director of Marketing Research, needs a sample of Kansas City households to participate in the testing of a new toothpaste package.If 40% of the households in Kansas City prefer the new package, the probability that Catherine's random sample of 300 households will have a sample proportion between 0.35 and 0.45 is closest to ___________.

Accepted Answer

Using the Central Limit Theorem, we can approximate the sampling distribution of the sample proportion with a normal distribution because the sample size is large (n=300). The mean of the sampling distribution is equal to the population proportion (p = 0.40), and the standard deviation (standard error) of the sampling distribution is sqrt[p(1-p)/n] = sqrt[0.40(0.60)/300] = 0.02887. We can use the normal distribution to find the probability that the sample proportion is between 0.35 and 0.45. Using a Z-score calculation for both 0.35 and 0.45 gives us Z-scores of (0.35-0.40)/0.02887 = -1.73 and (0.45-0.40)/0.02887 = 1.73, respectively. Looking up these Z-scores in a standard normal distribution table or using a calculator, we find that the area between these Z-scores is approximately 0.9232, indicating the probability.

Question 3

Suppose 65% of all college students have a laptop computer at home and a sample of 150 students is taken.The mean of the sampling distribution of $\hat { p }$ is

Accepted Answer

The mean of the sampling distribution of $\hat { p }$ (the sample proportion) is equal to the population proportion, which is given as 65% or 0.65.

Question 4

Alice Zhong is the VP of Operations at Pearl Financial Services.She wants to measure customer satisfaction after a new website and other changes were introduced a few months ago.For this purpose, she instructs her staff to prepare a questionnaire and send it to any IP address that accesses the company's website from 8 a.m.to 9 a.m.during each day of the next four weeks.This is an example of ______.

Accepted Answer

The answer of Alice Zhong is the VP of Operations...

Question 5

Alice Zhong is the VP of Operations at Pearl Financial Services.She wants to measure customer satisfaction after a new website and other changes were introduced a few months ago.For this purpose, she instructs her staff to prepare a questionnaire and send it to the first 200 clients in their alphabetical list of active clients.This is an example of ______.

Accepted Answer

Alice Zhong's method of selecting the first 200 clients from an alphabetical list is a convenience sample because it does not involve a random selection process. Instead, it selects a sample based on ease of access, which in this case is determined by the alphabetical order of the clients.

Question 6

Pinky Bauer, Chief Financial Officer of Harrison Haulers, Inc., suspects irregularities in the payroll system.If 10% of the 5,000 payroll vouchers issued since January 1, 2018, have irregularities, the probability that Pinky's random sample of 200 vouchers will have a sample proportion greater than .06 is closest to ___________.

Accepted Answer

The probability that a random sample of 200 vouchers will have a sample proportion greater than 0.06 can be found using the normal approximation to the binomial distribution. Given that 10% of the vouchers have irregularities, the expected proportion of irregularities in any sample is 0.10. The standard error (SE) of the sample proportion is calculated using the formula SE = sqrt[p(1-p)/n], where p is the proportion of interest (0.10) and n is the sample size (200). This gives SE = sqrt[0.10*0.90/200] = 0.0212. To find the probability that the sample proportion is greater than 0.06, we calculate the z-score for 0.06 using the formula z = (proportion - mean) / SE = (0.06 - 0.10) / 0.0212. The z-score corresponds to a probability in the lower tail, and the probability of interest is 1 minus this value. This calculation yields a probability close to 0.9706, indicating a high likelihood of finding a sample proportion greater than 0.06.

Question 7

Certain transportation company has a fleet of 210 vehicles.The average age of the vehicles is 4.25 years, with a standard deviation of 18 months.In a random sample of 40 vehicles, what is the probability that the average age of vehicles in the sample will be less than 4 years?

Accepted Answer

The correct answer is A because the probability that the average age of vehicles in the sample will be less than 4 years is 0.146.

Question 8

If random variable X is distributed according to a uniform distribution between 0 and 1 (X ~ U[0, 1]), and you take a random sample of size 35, what is the probability that the sample mean will fall between 0.48 and 0.55?

Accepted Answer

The answer of If random variable X is distributed according...

Question 9

Catherine Chao, Director of Marketing Research, needs a sample of Kansas City households to participate in the testing of a new toothpaste package.If 40% of the households in Kansas City prefer the new package, the probability that Catherine's random sample of 300 households will have a sample proportion greater than 0.45 is closest to ___________.

Accepted Answer

The answer of Catherine Chao, Director of Marketing Research, needs...

Question 10

The employees in certain division of Cybertronics Inc.need to complete a certification online.On average, it takes 20 hours to complete the coursework and successfully pass all tests, with a standard deviation of 6 hours.If you select a random sample of size 30, the probability that the employees in your sample have taken, on average, more than 20.5 hours is ______.

Accepted Answer

Using the Central Limit Theorem, we can calculate the probability that the sample mean is more than 20.5 hours. The standard error (SE) of the sample mean is the standard deviation divided by the square root of the sample size, which is $SE = \frac{6}{\sqrt{30}}$. To find the Z-score for 20.5 hours, we use the formula $Z = \frac{\bar{x} - \mu}{SE}$, where $\bar{x}$ is the sample mean (20.5 hours), and $\mu$ is the population mean (20 hours). Plugging in the values, we get a Z-score. Looking up this Z-score in the standard normal distribution table gives us the probability of observing a sample mean greater than 20.5 hours. The correct probability corresponds to option D, which is 0.32, indicating that there's a 32% chance the sample mean is more than 20.5 hours.

Question 11

In Norway, approximately 22% of vehicles are electric vehicles.Which is closest to the probability of randomly selecting 250 cars and finding out that 60 or more are electric?

Accepted Answer

The answer of In Norway, approximately 22% of vehicles are...

Question 12

Alice Zhong is the VP of Operations at Pearl Financial Services.She wants to measure customer satisfaction after a new website and other changes were introduced a few months ago.28% of clients are from the healthcare industry, 35% are manufacturing companies, 27% are financial firms, and 7% are construction companies.For this purpose, she gets random five-digits numbers from the website random.org (which offers true random numbers on the Internet).Then she uses these numbers to select 140 random clients from the healthcare sector, 175 from the manufacturing sector, 135 from the manufacturing sector, and 35 from the construction sector.This is an example of ______.

Accepted Answer

The answer of Alice Zhong is the VP of Operations...

Question 13

In an instant lottery, your chance of winning is 0.1.If you play the lottery 100 times and outcomes are independent, the probability that you win at least 15 percent of the time is closest to __________.

Accepted Answer

This problem can be approached using the binomial probability formula, which is P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successful outcomes, p is the probability of success on a single trial, and (n choose k) is the binomial coefficient. However, calculating the probability of winning exactly k times for k = 15, 16, ..., 100 directly would be cumbersome. Instead, we can use the normal approximation to the binomial distribution for large n, or recognize that the question asks for the probability of an event that is unlikely to happen given the parameters (winning rate of 0.1, but asking for at least a 0.15 win rate over 100 trials). Without doing the exact calculations, we can infer that the probability of winning at least 15 times out of 100, given a win probability of 0.1, is relatively low. Among the provided options, 0.0478 is the one that best fits this description, indicating a low probability event.

Question 14

Suppose 65% of all college students have a laptop computer at home and a sample of 150 is taken.The standard deviation of the sampling distribution of $\hat { p }$ is

Accepted Answer

The standard deviation of the sampling distribution of the sample proportion $\hat { p }$ is calculated using the formula $\sqrt{\frac{p(1-p)}{n}}$, where $p$ is the population proportion (0.65 in this case) and $n$ is the sample size (150). Plugging in the values, we get $\sqrt{\frac{0.65(1-0.65)}{150}} = \sqrt{\frac{0.65(0.35)}{150}} = \sqrt{\frac{0.2275}{150}} = \sqrt{0.0015167} \approx 0.0389$.

Question 15

If random variable X is distributed according to a uniform distribution between 0 and 1 (X ~ U[0, 1]), and 100 random samples of sizes 35-40 were taken, the standard deviation of the sample means would be ______.

Accepted Answer

The standard deviation of the sample means, also known as the standard error, is calculated as the population standard deviation divided by the square root of the sample size. For a uniform distribution U[0,1], the population standard deviation is 1/√12. For sample sizes between 35 and 40, the standard error will be between 0.0456 and 0.0488.

Question 16

If random variable X is distributed according to a uniform distribution between 0 and 1 (X ~ U[0, 1]), and 100 random samples of sizes 35-40 were taken, the sum of the sample means would be ______.

Accepted Answer

The expected value (mean) of a uniform distribution U[0, 1] is (0+1)/2 = 0.5. With 100 samples, the sum of the sample means is 100 * 0.5 = 50.0.

Question 17

Alice Zhong is the VP of Operations at Pearl Financial Services.She wants to measure customer satisfaction after a new website and other changes were introduced a few months ago.For this purpose, she uses random five-digits numbers from the website random.org (which offers true random numbers on the Internet).This is an example of ______.

Accepted Answer

Using random numbers from a website like random.org to select samples ensures that every element in the population has an equal chance of being selected, which is the definition of a simple random sample.

Quiz 7: Sampling and Sampling Distributions

Suppose 65% of all college students have a laptop computer at home and a sample of 150 students is taken.The mean of the sampling distribution of $\hat { p }$ is

Certain transportation company has a fleet of 210 vehicles.The average age of the vehicles is 4.25 years, with a standard deviation of 18 months.In a random sample of 40 vehicles, what is the probability that the average age of vehicles in the sample will be less than 4 years?

If random variable X is distributed according to a uniform distribution between 0 and 1 (X ~ U[0, 1]) , and you take a random sample of size 35, what is the probability that the sample mean will fall between 0.48 and 0.55?

In Norway, approximately 22% of vehicles are electric vehicles.Which is closest to the probability of randomly selecting 250 cars and finding out that 60 or more are electric?

In an instant lottery, your chance of winning is 0.1.If you play the lottery 100 times and outcomes are independent, the probability that you win at least 15 percent of the time is closest to __________.

Suppose 65% of all college students have a laptop computer at home and a sample of 150 is taken.The standard deviation of the sampling distribution of $\hat { p }$ is

If random variable X is distributed according to a uniform distribution between 0 and 1 (X ~ U[0, 1]) , and 100 random samples of sizes 35-40 were taken, the standard deviation of the sample means would be ______.

If random variable X is distributed according to a uniform distribution between 0 and 1 (X ~ U[0, 1]) , and 100 random samples of sizes 35-40 were taken, the sum of the sample means would be ______.

Quiz 7: Sampling and Sampling Distributions

Suppose 65% of all college students have a laptop computer at home and a sample of 150 students is taken.The mean of the sampling distribution of p^\hat { p }p^​ is

Certain transportation company has a fleet of 210 vehicles.The average age of the vehicles is 4.25 years, with a standard deviation of 18 months.In a random sample of 40 vehicles, what is the probability that the average age of vehicles in the sample will be less than 4 years?

If random variable X is distributed according to a uniform distribution between 0 and 1 (X ~ U[0, 1]) , and you take a random sample of size 35, what is the probability that the sample mean will fall between 0.48 and 0.55?

In Norway, approximately 22% of vehicles are electric vehicles.Which is closest to the probability of randomly selecting 250 cars and finding out that 60 or more are electric?

In an instant lottery, your chance of winning is 0.1.If you play the lottery 100 times and outcomes are independent, the probability that you win at least 15 percent of the time is closest to __________.

Suppose 65% of all college students have a laptop computer at home and a sample of 150 is taken.The standard deviation of the sampling distribution of p^\hat { p }p^​ is

If random variable X is distributed according to a uniform distribution between 0 and 1 (X ~ U[0, 1]) , and 100 random samples of sizes 35-40 were taken, the standard deviation of the sample means would be ______.

If random variable X is distributed according to a uniform distribution between 0 and 1 (X ~ U[0, 1]) , and 100 random samples of sizes 35-40 were taken, the sum of the sample means would be ______.

Suppose 65% of all college students have a laptop computer at home and a sample of 150 students is taken.The mean of the sampling distribution of $\hat { p }$ is

Suppose 65% of all college students have a laptop computer at home and a sample of 150 is taken.The standard deviation of the sampling distribution of $\hat { p }$ is