A survey of 25 randomly selected customers found the ages shown (in years). The mean is 32.48 years and the standard deviation is 9.60 years. 42 34 47 31 20 a) Construct a 95% confidence interval for the mean age of all customers, assuming that the assumptions and conditions for the confidence interval have been met. 40 29 45 27 38 b) How large is the margin of error? 29 33 49 37 31 c) How would the confidence interval change if you had assumed that the population standard deviation was known to be 10.0 years? 41 33 29 12 15 34 39 20 36 21 . . . . . a) What is the confidence interval? (Round to two decimal places as needed.)