In: Statistics and Probability

A study of the amount of time it takes a mechanic to rebuild the transmission for a 2010 Chevrolet Colorado 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 is less than 8.9 hours. Round to four decimal places. A.0.9756 B.0.9605 C.0.4276 D.0.9589

**SOLUTION:**

From given data,

**A study of the
amount of time it takes a mechanic to rebuild the transmission for
a 2010 Chevrolet Colorado 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 is less
than 8.9 hours.**

Where,

Population mean = = 8.4 hour

Population standard deviation = = 1.8 hour

Sample mean = = 8.9

Sample size = n = 40

Z = ( - ) / ( / )

= (8.9 - 8.4) / (1.8 / )

= 0.5 / 0.2846049

= 1.76

P(X < 8.9 ) = P(Z < 1.76 )

= 0.9605

Answer : Option (B) is correct

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