Question

The mean lifetime of a tire is 37 months with a standard deviation of 8 months. If 127 tires are sampled, what is the probability that the mean of the sample would be less than 38.85 months? Round your answer to four decimal places.

Answer 1

Solution :

Given that ,

mean =   = 37

standard deviation = = 8

n = 127

= 37

=  / n = 8/ 127=0.71

P( <38.85 ) = P[( - ) / < (38.85-37) / 0.71]

= P(z <2.61 )

Using z table  

=0.9955   

probability= 0.9955