# Hello,  can you help me with this math problem and show me step by step to understand this math problem. Thank you.In a random sample of 8, people the mean commute time to work was 36.5 mins and the standard deviation was 7.4 mins . A 98% confidence interval using the t-distribution was calculated (2.87, 44.3). After researching commute times to work, it was found that the population standard deviation is 8.8 mins. Find the margin of error and construct a 98% confidence interval using the standard normal distribution with the appropriate calculations for a standard deviation that is known. Compare the results.The margin of error of μ is________(Round to two decimal places as​ needed.)

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Hello,  can you help me with this math problem and show me step by step to understand this math problem. Thank you.

In a random sample of 8, people the mean commute time to work was 36.5 mins and the standard deviation was 7.4 mins . A 98% confidence interval using the t-distribution was calculated (2.87, 44.3). After researching commute times to work, it was found that the population standard deviation is 8.8 mins. Find the margin of error and construct a 98% confidence interval using the standard normal distribution with the appropriate calculations for a standard deviation that is known. Compare the results.

The margin of error of μ is________

(Round to two decimal places as​ needed.)

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Step 1

The provided values are:

Step 2

Here, the population standard deviation is known. So, we use the standard normal distribution.

The formula to calculate the confidence interval for the population mean is:

Step 3

The critical value at 98% confidence lev...

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