# (Solved) Math225 Week 6 Assignment: Confidence Interval for Mean – Population Standard Deviation Known

Question

Suppose scores of a standardized test are normally distributed and have a known population standard deviation of 11 points and an unknown population mean. A random sample of 15 scores is taken and gives a sample mean of 101 points. Find the confidence interval for the population mean with a 98% confidence level.

 z0.10 z0.05 z0.025 z0.01 z0.005 1.282 1.645 1.960 2.326 2.576

You may use a calculator or the common z values above.

• Round the final answer to two decimal places.

Question

Suppose the scores of a standardized test are normally distributed. If the population standard deviation is 2 points, what minimum sample size is needed to be 90% confident that the sample mean is within 1 point of the true population mean?

Use the table above for the z-score, and be sure to round up to the nearest integer.

Question

The length, in words, of the essays written for a contest are normally distributed with a population standard deviation of 442 words and an unknown population mean. If a random sample of 24 essays is taken and results in a sample mean of 1330 words, find a 99% confidence interval for the population mean.

You may use a calculator or the common z values above.

• Round the final answer to two decimal places.

Question

Suppose the heights of seasonal pine saplings are normally distributed. If the population standard deviation is 14 millimeters, what minimum sample size is needed to be 95% confident that the sample mean is within 4 millimeters of the true population mean?

Use the table above for the z-score, and be sure to round up to the nearest integer.

Question

The lengths, in inches, of adult corn snakes are normally distributed with a population standard deviation of 8 inches and an unknown population mean. A random sample of 25 snakes is taken and results in a sample mean of 58 inches.

What is the correct interpretation of the confidence interval?

Question

The lengths, in inches, of adult corn snakes are normally distributed with a population standard deviation of 8 inches and an unknown population mean. A random sample of 25 snakes is taken and results in a sample mean of 58 inches.

Identify the parameters needed to calculate a confidence interval at the 99% confidence level. Then find the confidence interval.

 z0.10z0.10 z0.05z0.05 z0.025z0.025 z0.01z0.01 z0.005z0.005 1.282 1.645 1.960 2.326 2.576

You may use a calculator or the common z values above.

• Round the final answer to two decimal places.

Question

The population standard deviation for the scores of a standardized test is 4 points. If we want to be 90% confident that the sample mean is within 1 point of the true population mean, what is the minimum sample size that should be taken?

Use the table above for the z-score, and be sure to round up to the nearest integer.

Question

The population standard deviation for the total snowfalls per year in a city is 13 inches. If we want to be 95% confident that the sample mean is within 3 inches of the true population mean, what is the minimum sample size that should be taken?

Use the table above for the z-score, and be sure to round up to the nearest integer.

# Solution:

Suppose scores of a standardized test are normally distributed and have a known population standard deviation of 11 points and an unknown population mean. A random sample of 15 scores is taken and gives a sample mean of 101 points. Find the confidence interval for the population mean with a 98% confidence level.

 z0.10 z0.05 z0.025 z0.01 z0.005 1.282 1.645 1.960 2.326 2.576

You may use a calculator or the common z values above.

• Round the final answer to two decimal places.