Question

A study of the amount of time it takes a mechanic to rebuild the transmission for a 2005 Chevrolet Cavalier shows that the mean is 8.6 hours and the standard deviation is 2.1 hours. If 36 mechanics are randomly selected, find the probability that their mean rebuild time exceeds 8.9 hours.

please add explanation and solve

Answer 1

Solution :

Given that ,

mean = = 8.6

standard deviation = = 2.1

n = 36

sample distribution of sample mean is ,

=

= 8.6

sampling distribution of standard deviation

=  / n = 2.1/ 36=0.35

= 0.35

P( > 8.9) = 1 - P( <8.9 )

= 1 - P[( - ) / < (8.9-8.6) / 0.35]

= 1 - P(z <0.86 )

Using z table

= 1 - 0.8051

= 0.1949

probability= 0.1949