# 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.)

Question

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.)