Question

A simple random sample of 12 iPhone's being sold over the Internet had the

following prices, in dollars.
287, 311, 262, 392, 313, 314, 257, 316, 286, 255, 283, 291
Assume that it is reasonable to believe that the population is approximately normal
and the population standard deviation is 56. What is the upper bound of the 95%
confidence interval for the mean price for all phones of this type?
Round your answer to one decimal places (for example: 319.4).

Answer 1

The upper bound is 399.5

Explanation:

Let's start by calculating the mean value of the distribution as the addition of all values given divided by 12:

Average = 289.75.

If the standard deviation is 56, then the upper bound in 95% the confidence interval for the mean price of the phones is going to be given by the mean value added to 56 times 1.96 (since 95% of the population is withing 1.96 times the standard deviation)

That is: 289.75 + 56 * 1.96 = 399.51

which rounded to one decimal place gives: 399.5