A certain brand of automobile tire has a mean life span of 32,000 miles and a standard deviation of 2,450 miles. (Assume the life spans of the tires have a bell-shaped distribution.) (a) The life spans of three randomly selected tires are 34,000 miles, 37,000 miles, and 31,000 miles. Find the z-score that corresponds to each life span.

a)

The z-score corresponds to 34000 is 0.816

The z-score corresponds to 37000 is 2.041

The z-score corresponds to 31000 is - 0.408

Step-by-step explanation:

The z-score corresponds to 34000

Let x=34000

z-score = (x-mean) / standard deviation

z-score=34000-32000/2450=0.816

The z-score corresponds to 34000 is 0.816

The z-score corresponds to 37000

Let x=37000

z-score = (x-mean) / standard deviation

z-score=37000-32000/2450=2.041

The z-score corresponds to 37000 is 2.041

The z-score corresponds to 31000

Let x=31000

z-score = (x-mean) / standard deviation

z-score=31000-32000/2450=-0.408

The z-score corresponds to 31000 is - 0.408