The mean life span of a brand name tire is 50000 miles Assum

The mean life span of a brand name tire is 50,000 miles. Assume that the life spans of the tires are normally distributed, and the population standard deviation is 800 miles.

(a). If you select 100 tires, what is the probability that their mean life span is less than 50,200 miles?

(b). If you select 100 tires, what is the probability that their mean life span is greater than 50,200 miles?

(c). ). If you select 100 tires, what is the probability that their mean life span is between 48,500 miles and 50,200 miles?

Solution

Solution :

Mean =50000

SD = 800

(a)

P(X<50200)

z = (50200-50000)/(800/sqrt(100)) = 2.5

Therefore

P-value = 0.9938 Answer

(b)

P(X>50200)

z = (50200-50000)/(800/sqrt(100)) = 2.5

Therefore

P-value = 1 - 0.9938 = 0.0062 Answer

(c)

P(4850<X<50200)

z1 = (50200-50000)/(800/sqrt(100)) = 2.5

z2 = (48500-50000)/(800/sqrt(100)) = -18.75

P-value = 0.9938 - (~0) = 0.9938 Answer