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. Suppose 40 mechanics are randomly selected, what is the probability the average time to rebuild the transmission of a 1992 Chevrolet Cavalier for these 40 mechanics is more than 8.1 hours?

Answer 1

Solution :

Given that ,

mean = = 8.4

standard deviation = = 1.8

n = 40

= 8.4

= / n = 1.8 / 40 = 0.28

P( > 8.1) = 1 - P( < 8.1)

= 1 - P[( - ) / < (8.1-8.4) /0.28 ]

= 1 - P(z < -1.07)

Using z table

= 1 - 0.1423

= 0.8577

probability= 0.8577