Question

Two engineers, Philip and Ayazi, are given access to 45 prototype car tires to test for mileage lifetime. Philip tests all 45 tires and determines that tire performance is normally distributed with an average lifetime of 60,000 miles and standard deviation of 8,000 miles Their supervisor wants to tell the company's Board of Directors that this batch of prototype tires will last at least 50,000 miles. ) What can Philip state about the tires lasting at least 50,000 miles? b) What can Philip state about the mileage that 95% percentage of tires will last

Answer 1

(a)

= 60,000

= 8,000

n = 45

SE = /

= 8,000/ = 1192.5696

To find P(50,000)

Z = (50,000 - 60,000)/1192.5696 = - 8.3853

Table of Area Under Standard Normal Curve gives area = 0.5 nearly

So,

P(50,000) = .05 nearly + 0.05 = 1.0 nearly

(b)

= 60,000

= 8,000

n = 45

SE = /

= 8,000/ = 1192.5696

95% corresponds to area = 0.95 - 0.50 = 0.45 from mid value to Z on RHS.

Table of Area Under Standard Normal Curve gives Z = 1.645

Z = 1.645 = (X - 60,000)/1192.5696

So,

X = 60,000 + (1.645 X 1192.5696)

= 60,000 + 1961.7770

= 61,961.7770

So,

Answer is:

61,961.7770