
An electronics magazine reports that a 90% confidence interval for the mean price of GPS navigation systems is $178.75 to $211.87. Using the confidence interval, find the sample mean and the margin of error.

The confidence interval is from $178.75 to $211.87. Recall that a confidence interval is given by
Sample mean ± margin of error.
The sample mean is the value in the middle of the confidence interval. To find the value that is in the middle of two numbers, add the numbers and divide by 2 as shown below.
To find the margin of error, subtract the sample mean from $211.87 because the distance from the sample mean to the right endpoint of the confidence interval is the margin of error.
So, the sample mean is $195.31 and the margin of error is $16.56.
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A state agency reports that a 95% confidence interval for the mean annual salaries of employees in Colorado is $45,832 to $47,890. Using the confidence interval, find the sample mean and the margin of error.
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A hospital reports that a 99% confidence interval for the mean length of stay (in days) of patients is 5.1 to 5.9. Using the confidence interval, find the sample mean and the margin of error.

The confidence interval is from 5.1 days to 5.9 days. Recall that a confidence interval is given by
Sample mean ± margin of error.
The sample mean is the value in the middle of the confidence interval. To find the value that is in the middle of two numbers, add the numbers and divide by 2 as shown below.
To find the margin of error, subtract the sample mean from 5.9 days because the distance from the sample mean to the right endpoint of the confidence interval is the margin of error.
So, the sample mean is 5.5 days and the margin of error is 0.4 day.
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A company reports that a 95% confidence interval for the mean weight (in ounces) of filled paint cans is 159.97 to 160.03. Using the confidence interval, find the sample mean and the margin of error.
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For a 95% confidence level, the minimum sample size n needed to estimate the population mean is
where E is the margin of error and s is the population standard deviation. You want to estimate the mean weight of newborns within 0.25 pound of the population mean. Assume the population standard deviation is 1.3 pounds. Find the minimum sample size. If necessary, round your answer up to a whole number.

You have the following information.
Use the formula for minimum sample size.
Rounding up, the minimum sample size is 104 newborns.
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For a 95% confidence level, the minimum sample size n needed to estimate the population mean is
where E is the margin of error and s is the population standard deviation. You want to estimate the mean number of text messages sent per day by 18 to 24yearolds within 5 messages of the population mean. Assume the population standard deviation is 30 messages. Find the minimum sample size. If necessary, round your answer up to a whole number.
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For a 95% confidence level, the minimum sample size n needed to estimate the population mean is
where E is the margin of error and s is the population standard deviation. You want to estimate the mean number of hours of television watched per person per day within 0.1 hour of the population mean. Assume the population standard deviation is 1.5 hours. Find the minimum sample size. If necessary, round your answer up to a whole number.

You have the following information.
Use the formula for minimum sample size.
Rounding up, the minimum sample size is 865 people.
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For a 95% confidence level, the minimum sample size n needed to estimate the population mean is
where E is the margin of error and s is the population standard deviation. You want to estimate the mean number of minutes waiting at a department of motor vehicles office within 0.5 minute of the population mean. Assume the population standard deviation is 7 minutes. Find the minimum sample size. If necessary, round your answer up to a whole number.
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