Each year an airline selects a simple random sample of 475 customers in their frequent flyer program in order to learn about the number of miles they fly. The historical data indicates that the population follows a normal distribution.

Last year, they monitored 475 frequent flyers (n= 475) and obtained a sample mean of (x )= 27,601 miles. Based on historical data, they now assume a known value of = 583 miles. The confidence coefficient to be used in the interval estimate is .95.

What will the margin of error be for their 95% confidence interval?

ROUND TO TWO DECIMAL PLACES