The mean price goes between $ 41.16 and $ 42.84, so a value of $ 48 is unusually high.
Since the average price of an item is $ 42 with a standard deviation of $ 3, to find a 98% confidence interval about the mean, and determine if a value of X = 48 is unusually high or if it is normal, the following calculations should be done:
(((42 - 3) + (42 + 3)) / 2) x 0.98 = X
((39 + 45) / 2) x 0.98 = X
42 x 0.98 = X
41.16 = X
(((42 - 3) + (42 + 3)) / 2) x 1.02 = X
((39 + 45) / 2) x 1.02 = X
42 x 1.02 = X
42.84 = X
Therefore, as the mean price goes between $ 41.16 and $ 42.84, a value of $ 48 is unusually high.
