Question 1

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

Accepted Answer

The probability of selecting 60 or more electric vehicles out of 250 can be calculated using the binomial distribution. With a probability of 0.22 for each car being electric, the probability of 60 or more is approximately 0.223.

Question 2

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

Accepted Answer

This is a binomial distribution problem, where n = 100 (the number of trials), p = 0.1 (the probability of winning), and we want to find the probability of winning at least 15 times (or 15% of the time). Using the binomial distribution formula, the probability is: P(X >= 15) = 1 - P(X < 15) Where X is the number of times we win in 100 trials. Using a binomial probability table or calculator, we can find: P(X < 15) = 0.9522 (rounded to four decimal places) So, P(X >= 15) = 1 - 0.9522 = 0.0478 Therefore, the answer is D.

Question 3

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 clients that access the company's website during from 8 a.m.to 9 a.m.for the next four weeks.This is an example of ______.

Accepted Answer

This is an example of a convenience sample because the VP of operations instructed her staff to send the questionnaire to clients that access the website between 8 a.m. and 9 a.m. This sampling method is convenient and does not involve a random selection process.

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.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 5

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,and the standard deviation is 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

The answer of The employees in certain division of Cybertronics...

Question 6

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  is

Accepted Answer

The mean of the sampling distribution of proportions is equal to the true population proportion. Therefore, the mean of the sampling distribution of the proportion of college students who have a laptop computer at home will be equal to 0.65, based on the given information. So, the best choice is A) 0.65.

Question 7

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 8

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  is

Accepted Answer

The answer of Suppose 65% of all college students have...

Question 9

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 can be calculated using the formula:
standard deviation = standard deviation of population / square root of sample size
Since X ~ U[0,1], the standard deviation of the population can be calculated as:
standard deviation of population = (1-0)/sqrt(12) = 0.2887
Using the largest sample size of 40, the standard deviation of the sample means would be:
standard deviation = 0.2887 / sqrt(40) = 0.0457
Using the smallest sample size of 35, the standard deviation of the sample means would be:
standard deviation = 0.2887 / sqrt(35) = 0.0488
Therefore, the standard deviation of the sample means would be between 0.0488 and 0.0457, which corresponds to answer choice C.

Question 10

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 11

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

This is an example of a simple random sample, as random numbers are being used to select participants without any specific criteria or bias.

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.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

This is an example of a convenience sample because the clients are chosen based on their availability and ease of access rather than randomly selecting from the entire population or a specific stratum. This method may lead to biases as certain types of clients may be more likely to respond to the questionnaire.

Question 13

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 answer of Certain transportation company has a fleet of...

Quiz 7: Sampling and Sampling Distributions

In Norway,approximately 22% of vehicles are electric vehicles.What is 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

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 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 sum of the sample means would be ______.

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 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 you take a random sample of size 35,what is the probability that the sample mean will fall between 0.48 and 0.55?

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?