Question

The mean lifetime of a tire is 42 months with a standard deviation of 55 months.

If 117 tires are sampled, what is the probability that the mean of the sample would be greater than 42.72 months? Round your answer to four decimal places.

Answer 1

Solution :

Given that ,

mean = = 42

standard deviation = = 55

n = 117

= 42

= / n = 55/ 117 = 5.08

P( >42.72 ) = 1 - P( < 42.72)

= 1 - P[( - ) / < (42.72-42) /5.08 ]

= 1 - P(z <0.14 )

Using z table

= 1 - 0.5557

= 0.4443

probability= 0.4443