Answer to Question #65601 in Statistics and Probability for devangi

Question

A bank wishing to determine the average amount of time a customer must wait to be
served took a random sample of 100 customers and found that the mean waiting time
was 7.2 minutes. Assuming that the population standard deviation is known to be
15 minutes, find the 90% confidence interval estimate of the mean waiting time for
all the bank’s customers.

Answer 1

Due to the central limit theorem distribution of the sum of stochastic variables converges to the normal distribution.
Therefore, it is possible to approximate the solution with the normal distribution.
The formula for the confidence interval will be:
(mean - z_(1-alpha/2) * sd / sqrt(n), mean - z_(1-alpha/2) * sd / sqrt(n))
where mean = 7.2, sd = 15
z_(1 - alpha) = 1.645
n = 100

Thus, the confidence interval is: (4.73, 9.67)