**Week 6 Assignment Confidence Interval for Mean**

**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.

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

Round the final answer to two decimal places

Provide your answer below:

**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.

Provide your answer below:

**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.

Provide your answer below:

**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.

Provide your answer below:

So we estimate with 99% confidence that the true population mean is between 1097.59 and 1562.41 words.

**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.

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

- Round the final answer to two decimal places.

Provide your answer below:

**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?

Select the correct answer below:

We can estimate with 99% confidence that the true population mean length of adult corn snakes is between 53.88 and 62.12 inches.

We can estimate with 99% confidence that the sample mean length of adult corn snakes is between 53.88 and 62.12 inches.

We can estimate that 99% of adult corn snakes will have a length that is between 53.88 and 62.12 inches.

**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.

Provide your answer below:

**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.

Provide your answer below:

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