Question 1

Magazines 
A local magazine store sells an average of 2,100 magazines per day,with a standard deviation of 500 magazines.Consider a sample of 60 days of operation.
-{Magazines Narrative} Find the expected value and the standard error of the sample mean.

Accepted Answer

The answer of  Magazines 
A local magazine store sells...

Question 2

Recall the rule of thumb used to indicate when the normal distribution is a good approximation of the sampling distribution for the sample proportion  .For the combination n = 50,p = 0.05,the rule is satisfied.

Accepted Answer

The answer of Recall the rule of thumb used to...

Question 3

In general,the binomial probability P(X = x)is approximated by the area under a normal curve between x − .5 and x + .5.

Accepted Answer

This is known as the continuity correction in approximating binomial probabilities with a normal distribution.

Question 4

A CPA knows from past history that the average accounts receivable for a company is $521.72 with a standard deviation of $584.64.If the auditor takes a simple random sample of 100 accounts,what is the probability that the mean of the sample is within $120 of the population mean?

Accepted Answer

The answer of A CPA knows from past history that...

Question 5

The standard error of the sampling distribution of the sample proportion  ,when the sample size n = 100 and the population proportion p = 0.30,is 0.0021.

Accepted Answer

The answer of The standard error of the sampling distribution...

Question 6

Magazines 
A local magazine store sells an average of 2,100 magazines per day,with a standard deviation of 500 magazines.Consider a sample of 60 days of operation.
-{Magazines Narrative} What is the shape of the sampling distribution of the sample mean number of magazines sold per day? Why?

Accepted Answer

The answer of  Magazines 
A local magazine store sells...

Question 7

In general,the binomial probability P(X ≥ x)is approximated by the area under the normal curve to the left of x − .5.

Accepted Answer

The binomial probability P(X ≥ x) is approximated by the area under the normal curve to the right of x - .5, not to the left. This adjustment, known as the continuity correction, helps align discrete binomial outcomes with the continuous normal distribution.

Question 8

As a general rule,the normal distribution is used to approximate the sampling distribution of the sample proportion only if the sample size n is greater than or equal to 30.

Accepted Answer

The normal distribution is used to approximate the sampling distribution of the sample proportion if the sample size is large enough so that both np and n(1-p) are greater than or equal to 10, where n is the sample size and p is the population proportion. The rule of n ≥ 30 typically applies to the sampling distribution of the sample mean, not the sample proportion.

Question 9

If a simple random sample of 300 observations is taken from a population whose proportion p = 0.6,then the expected value of the sample proportion  is 0.60.

Accepted Answer

The expected value of the sample proportion is equal to the population proportion, which is 0.6 in this case.

Question 10

Number of Fish Tanks 
The following data give the number of fish tanks owned for a population of 4 families.  ​ ​
-{Number of Fish Tanks Narrative} List all possible samples of 2 families that can be selected without replacement from this population,and compute the sample mean  for each sample.

Accepted Answer

The answer of  Number of Fish Tanks 
The following...

Question 11

In general,the binomial probability P(X ≤ x)is approximated by the area under the normal curve to the left of x + .5.

Accepted Answer

This is known as the continuity correction for approximating a binomial distribution with a normal distribution. The area under the normal curve to the left of x + 0.5 is a good approximation for the probability of getting x or fewer successes in a binomial experiment with n trials and probability of success p, assuming certain conditions are met.

Question 12

In an effort to identify the true proportion of college freshman who are under 18 years of age,a random sample of 500 freshmen was taken.Fifty of them were under the age of 18.The value 0.10 is a point estimate of the true proportion of freshman under age 18.

Accepted Answer

The point estimate for the proportion is calculated by dividing the number of freshmen under 18 (50) by the total number of freshmen sampled (500), which equals 0.10.

Question 13

Number of Fish Tanks 
The following data give the number of fish tanks owned for a population of 4 families.  ​ ​
-{Number of Fish Tanks Narrative} A sample of size 2 is drawn at random from the population.Use the formulas  and  to calculate the mean and the standard deviation of the sampling distribution of the sample means.
​

Accepted Answer

The answer of  Number of Fish Tanks 
The following...

Question 14

Number of Fish Tanks 
The following data give the number of fish tanks owned for a population of 4 families.  ​ ​
-{Number of Fish Tanks Narrative} Find the mean and the standard deviation for the population.

Accepted Answer

The answer of  Number of Fish Tanks 
The following...

Question 15

In a given year,the average annual salary of a NHL hockey player was $205,000 with a standard deviation of $24,500.If a simple random sample of 50 players was taken,what is the probability that the sample mean will exceed $210,000?

Accepted Answer

The answer of In a given year,the average annual salary...

Question 16

The mean of the sampling distribution of the sample proportion  ,when the sample size n = 100 and the population proportion p = 0.92,is 92.0.

Accepted Answer

The answer of The mean of the sampling distribution of...

Question 17

Magazines 
A local magazine store sells an average of 2,100 magazines per day,with a standard deviation of 500 magazines.Consider a sample of 60 days of operation.
-{Magazines Narrative} What is the probability that the sample mean is between 2,000 and 2,300 magazines?

Accepted Answer

The answer of  Magazines 
A local magazine store sells...

Question 18

Given that X is a binomial random variable with very large n,the binomial probability P(X = 5)is approximated by the area under a normal curve between

Accepted Answer

When n is large, the binomial distribution can be approximated by a normal distribution with mean μ = np and standard deviation σ = √(np(1-p)). The continuity correction can be applied to approximate the probability of X = 5 as the area under the normal curve between 4.5 and 5.5. This is because we are looking for the probability that X takes on a specific value (5) and not a range of values. Option A is incorrect because the area under a normal curve at a specific point is always zero. Option B is incorrect because it is too broad for the specific probability we are looking for. Option D is incorrect because there is a best choice among the options given.

Question 19

Number of Fish Tanks 
The following data give the number of fish tanks owned for a population of 4 families.  ​ ​
-{Number of Fish Tanks Narrative} Find the sampling distribution of  ,and use it to calculate the mean and the standard deviation of  .

Accepted Answer

The answer of  Number of Fish Tanks 
The following...

Question 20

Given that X is a binomial random variable with very large n,the binomial probability P(X ≥ 5)is approximated by the area under a normal curve to the right of

Accepted Answer

When approximating a binomial distribution with a normal distribution for a binomial random variable X, the continuity correction factor is used. For P(X ≥ 5), the correct continuity correction is to look for the area under the normal curve to the right of 4.5. This accounts for the fact that the binomial distribution is discrete, while the normal distribution is continuous.

Quiz 9: Sampling Distributions

Magazines A local magazine store sells an average of 2,100 magazines per day,with a standard deviation of 500 magazines.Consider a sample of 60 days of operation. -{Magazines Narrative} Find the expected value and the standard error of the sample mean.

Recall the rule of thumb used to indicate when the normal distribution is a good approximation of the sampling distribution for the sample proportion .For the combination n = 50,p = 0.05,the rule is satisfied.

In general,the binomial probability P(X = x)is approximated by the area under a normal curve between x − .5 and x + .5.

A CPA knows from past history that the average accounts receivable for a company is $521.72 with a standard deviation of $584.64.If the auditor takes a simple random sample of 100 accounts,what is the probability that the mean of the sample is within $120 of the population mean?

The standard error of the sampling distribution of the sample proportion ,when the sample size n = 100 and the population proportion p = 0.30,is 0.0021.

Magazines A local magazine store sells an average of 2,100 magazines per day,with a standard deviation of 500 magazines.Consider a sample of 60 days of operation. -{Magazines Narrative} What is the shape of the sampling distribution of the sample mean number of magazines sold per day? Why?

In general,the binomial probability P(X ≥ x)is approximated by the area under the normal curve to the left of x − .5.

As a general rule,the normal distribution is used to approximate the sampling distribution of the sample proportion only if the sample size n is greater than or equal to 30.

If a simple random sample of 300 observations is taken from a population whose proportion p = 0.6,then the expected value of the sample proportion is 0.60.

Number of Fish Tanks The following data give the number of fish tanks owned for a population of 4 families. -{Number of Fish Tanks Narrative} List all possible samples of 2 families that can be selected without replacement from this population,and compute the sample mean for each sample.

In general,the binomial probability P(X ≤ x)is approximated by the area under the normal curve to the left of x + .5.

In an effort to identify the true proportion of college freshman who are under 18 years of age,a random sample of 500 freshmen was taken.Fifty of them were under the age of 18.The value 0.10 is a point estimate of the true proportion of freshman under age 18.

Number of Fish Tanks The following data give the number of fish tanks owned for a population of 4 families. -{Number of Fish Tanks Narrative} Find the mean and the standard deviation for the population.

In a given year,the average annual salary of a NHL hockey player was $205,000 with a standard deviation of $24,500.If a simple random sample of 50 players was taken,what is the probability that the sample mean will exceed $210,000?

The mean of the sampling distribution of the sample proportion ,when the sample size n = 100 and the population proportion p = 0.92,is 92.0.

Magazines A local magazine store sells an average of 2,100 magazines per day,with a standard deviation of 500 magazines.Consider a sample of 60 days of operation. -{Magazines Narrative} What is the probability that the sample mean is between 2,000 and 2,300 magazines?

Given that X is a binomial random variable with very large n,the binomial probability P(X = 5) is approximated by the area under a normal curve between

Number of Fish Tanks The following data give the number of fish tanks owned for a population of 4 families. -{Number of Fish Tanks Narrative} Find the sampling distribution of ,and use it to calculate the mean and the standard deviation of .

Given that X is a binomial random variable with very large n,the binomial probability P(X ≥ 5) is approximated by the area under a normal curve to the right of

Quiz 9: Sampling Distributions

Magazines A local magazine store sells an average of 2,100 magazines per day,with a standard deviation of 500 magazines.Consider a sample of 60 days of operation. -{Magazines Narrative} Find the expected value and the standard error of the sample mean.

Recall the rule of thumb used to indicate when the normal distribution is a good approximation of the sampling distribution for the sample proportion .For the combination n = 50,p = 0.05,the rule is satisfied.

In general,the binomial probability P(X = x)is approximated by the area under a normal curve between x − .5 and x + .5.

A CPA knows from past history that the average accounts receivable for a company is $521.72 with a standard deviation of $584.64.If the auditor takes a simple random sample of 100 accounts,what is the probability that the mean of the sample is within $120 of the population mean?

The standard error of the sampling distribution of the sample proportion ,when the sample size n = 100 and the population proportion p = 0.30,is 0.0021.

Magazines A local magazine store sells an average of 2,100 magazines per day,with a standard deviation of 500 magazines.Consider a sample of 60 days of operation. -{Magazines Narrative} What is the shape of the sampling distribution of the sample mean number of magazines sold per day? Why?

In general,the binomial probability P(X ≥ x)is approximated by the area under the normal curve to the left of x − .5.

As a general rule,the normal distribution is used to approximate the sampling distribution of the sample proportion only if the sample size n is greater than or equal to 30.

If a simple random sample of 300 observations is taken from a population whose proportion p = 0.6,then the expected value of the sample proportion is 0.60.

Number of Fish Tanks The following data give the number of fish tanks owned for a population of 4 families. ​ ​ -{Number of Fish Tanks Narrative} List all possible samples of 2 families that can be selected without replacement from this population,and compute the sample mean for each sample.

In general,the binomial probability P(X ≤ x)is approximated by the area under the normal curve to the left of x + .5.

In an effort to identify the true proportion of college freshman who are under 18 years of age,a random sample of 500 freshmen was taken.Fifty of them were under the age of 18.The value 0.10 is a point estimate of the true proportion of freshman under age 18.

Number of Fish Tanks The following data give the number of fish tanks owned for a population of 4 families. ​ ​ -{Number of Fish Tanks Narrative} Find the mean and the standard deviation for the population.

In a given year,the average annual salary of a NHL hockey player was $205,000 with a standard deviation of $24,500.If a simple random sample of 50 players was taken,what is the probability that the sample mean will exceed $210,000?

The mean of the sampling distribution of the sample proportion ,when the sample size n = 100 and the population proportion p = 0.92,is 92.0.

Magazines A local magazine store sells an average of 2,100 magazines per day,with a standard deviation of 500 magazines.Consider a sample of 60 days of operation. -{Magazines Narrative} What is the probability that the sample mean is between 2,000 and 2,300 magazines?

Given that X is a binomial random variable with very large n,the binomial probability P(X = 5) is approximated by the area under a normal curve between

Number of Fish Tanks The following data give the number of fish tanks owned for a population of 4 families. ​ ​ -{Number of Fish Tanks Narrative} Find the sampling distribution of ,and use it to calculate the mean and the standard deviation of .

Given that X is a binomial random variable with very large n,the binomial probability P(X ≥ 5) is approximated by the area under a normal curve to the right of

Number of Fish Tanks The following data give the number of fish tanks owned for a population of 4 families. -{Number of Fish Tanks Narrative} List all possible samples of 2 families that can be selected without replacement from this population,and compute the sample mean for each sample.

Number of Fish Tanks The following data give the number of fish tanks owned for a population of 4 families. -{Number of Fish Tanks Narrative} Find the mean and the standard deviation for the population.

Number of Fish Tanks The following data give the number of fish tanks owned for a population of 4 families. -{Number of Fish Tanks Narrative} Find the sampling distribution of ,and use it to calculate the mean and the standard deviation of .