Answer to Question #190639 in Statistics and Probability for Ellyza jane

Question

The number of driving miles before a certain kind of life begins to show wear is on the average, 16,800 miles with a standard deviation of 3,300 miles. a. What is the probability that the 36 tires will have an average of less than 16,000 miles until the tires begin to wear out? b. What is the probability that the 36 tires will have an average of more than 18,000 miles until the tirea begin to wear out?

Answer 1

We have that:

$\mu=16800$

$\sigma=3300$

$n=36$

a) $P(\bar X<16000)=P(Z<\dfrac{x-\mu}{\frac{\sigma}{\sqrt n}})=P(Z<\dfrac{16000-16800}{\frac{3300}{\sqrt {36}}})=P(Z<-1.45)=0.0735$

b)

 $P(\bar X>18000)=1-P(\bar X < 18000)\\[9pt]=1-P(Z<\dfrac{18000-16800}{\frac{3300}{\sqrt {36}}})\\[9pt]=1-P(Z<2.18)\\[9pt]=1-0.9854=0.0146$