Central Limit Theorem Practice

Describe the shape of the sampling distribution of x-bar for SRSs of size n = 15 from the population of homeowners. Justify your answer.

• Because n = 15, the sampling distribution of x-bar will also be skewed to the right, but not quite as strongly as the population.

• Because n = 15, the sampling distribution of x-bar will be approximately normal.

• Because n = 15, the sampling distribution of x-bar will be heavily skewed to the left.

Describe the shape of the sampling distribution of x-bar for SRSs of size n = 10, 000 from the population of homeowners. Justify your answer.

• Because n = 10,000, the sampling distribution of x-bar is approximately normal by the central limit theorem.

• Because n = 10,000, the sampling distribution of x-bar is heavily skewed left.

• Because n = 10,000, the sampling distribution of x-bar is heavily skewed right.

Could the distribution of the number of people per car be approximately normal for the population of cars entering the interchange during rush hours? Explain your answer.

No. In a normal distribution, the minimum is __________ standard deviations below the mean.

• at least 2

• exactly 2

• less than 1

• less than 2

Describe the shape of the sampling distribution of x-bar for SRSs of size n = 100 from the population of cars that enter this interchange during rush hours. Justify your answer.

Because n = 100, the sampling distribution of x-bar

is ______________________.

• approximately normal by the central limit theorem.

• heavily skewed right.

• heavily skewed left.

Describe the shape of the sampling distribution of x-bar for samples of size 10,000.

• Approximately normal

  because of the central limit theorem.

• Approximately normal

  because the population is approximately normal.

• Skewed right because the population is heavily skewed right.

Describe the center of the sampling distribution of x-bar for samples of size 10,000.

$________

Describe the variability of the sampling distribution of x-bar for samples of size 10,000.

$_________

Suppose that the insurance company charges $300 for each policy. What is the probability that the insurance company will make money on a random sample of 10,000 homeowners?

    That is, what is the probability that the mean loss for a random sample of homeowners is less than $300?

  (Enter your answer as a decimal, rounded to 4 decimal places. Using normalcdf on the calculator is recommended.)

Describe the shape of the sampling distribution of x-bar for samples of size 100.

• Approximately normal

  because of the central limit theorem.

• Approximately normal

  because the population is approximately normal.

• Skewed right because the population is heavily skewed right.

Describe the center of the sampling distribution of x-bar for samples of size 100.