Fifteen smart cars were randomly selected and the highway mileage of each was noted. The analysis yielded a mean of 47 miles per gallon and a standard deviation of 5 miles per galon. Which of the following would represent a 90% confidence interval for the average highway mileage of all SmartCars?

Question

The correct answer is:

47-/+1.761(5/√15)

but my question is: how do you get 1.761?

Thanks

Answer 1

On a normal distributed cureve, mean=0, the standard deviation to have for a 90% confidence interval for the mean µ is t0.05,14 = 1.761 . The "cumulative probability" to the left of 1.76 is 0.95, and the probability to the right of 1.76 is 0.05.