Question

A study of the amount of time it takes a mechanic to rebuild the transmission for a 1992 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected, find the probability that their mean rebuild time exceeds 7.7 hours.

A. 0.8531

B. 0.9634

C. 0.9712

D. 0.9931

Answer 1

Solution :

Given that ,

mean = = 8.4

standard deviation = = 1.8

n = 40

= 8.4

= / n = 1.8/ 40 = 0.2846

P( >7.7 ) = 1 - P( <7.7)

= 1 - P[( - ) / < (7.7 - 8.4 ) /0.2846 ]

= 1 - P(z < -2.46)

Using z table,    

= 1 - 0.0069

=0.9931

probability= 0.9931

correct answer is D. 0.9931