(ANSWER) MATH 225N-Week 6 Assignment Confidence Interval for Mean Population Standard Deviation Known - Essay Prowess
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# (ANSWER) MATH 225N-Week 6 Assignment Confidence Interval for Mean Population Standard Deviation Known

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## Question1

Suppose finishing time for cyclists in a race are normally distributed and have a known population standard deviation of 6 minutes and an unknown population mean. A random sample of 18 cyclists is taken and gives a sample mean of 146 minutes.

Find the confidence interval for the population mean with a 99% confidence level.

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 2

The number of square feet per house are normally distributed with a population standard deviation of 154 square feet and an unknown population mean. If a random sample of 16 houses is taken and results in a sample mean of 1550 square feet, find a 80% confidence interval for the population mean.

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 3

Suppose the finishing times for cyclists in a race are normally distributed. If the population standard deviation is 16 minutes, what minimum sample size is needed to be 90% confident that the sample mean is within 5 minutes of the true population mean?

z0.101.282z0.051.645z0.0251.960z0.012.326z0.0052.576

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

## Question 4

Suppose the finishing times for cyclists in a race are normally distributed. If the population standard deviation is 16 minutes, what minimum sample size is needed to be 90% confident that the sample mean is within 5 minutes of the true population mean?

z0.101.282z0.051.645z0.0251.960z0.012.326z0.0052.576

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

## Question 5

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 6

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?

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.

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

Once a confidence interval is calculated, the interpretation should clearly state the confidence level (CL), explain what population parameter is being estimated, and state the confidence interval.

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

## Question 7

Suppose the germination periods, in days, for grass seed are normally distributed. If the population standard deviation is 3 days, what minimum sample size is needed to be 90% confident that the sample mean is within 1 day of the true population mean?

z0.101.282z0.051.645z0.0251.960z0.012.326z0.0052.576

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

## Question 8

Suppose the weights, in pounds, of the dogs in a city are normally distributed. If the population standard deviation is 3 pounds, what minimum sample size is needed to be 95% confident that the sample mean is within 1 pound of the true population mean?

z0.101.282z0.051.645z0.0251.960z0.012.326z0.0052.576

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