The tread lives of the Super Titan radial tires under normal driving conditions

Question

The tread lives of the Super Titan radial tires under normal driving conditions are normally distributed with a mean of 60,000 mi and a standard deviation of 6000 mi. (Round your answers to four decimal places.)

a) What is the probability that a tire selected at random will have a tread life of more than 52,200 mi?


b) Determine the probability that four tires selected at random still have useful tread lives after 52,200 mi of driving. (Assume that the tread lives of the tires are independent of each other.)


You may need to use the appropriate table in the Appendix of Tables to answer this question.

Explanation / Answer

a) Given Data

mean=60,000 mi

and std.dev.=6000 mi

now for tread life more than 52,000

Z score for 52,200=(52,200-60,000)/6000

= -1.3

now P(Z<-1.3)=.09176 --------------(from STANDARD NORMAL DISTRIBUTION Table)

so probability of tread life greater than 52,200=1-.09176

=.90824 ANS.

b) For 4 tires selected randomly have live more than 52,200=(.90824)^4

= .6805

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