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In: Statistics and Probability

A study of the amount of time it takes a mechanic to rebuild the transmission for...

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

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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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