A study of the amount of time it takes a mechanic to rebuild the transmission fo
ID: 2933922 • Letter: A
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 a Chevrolet Cavalier is randomly selected, find the probability that its rebuild time exceeds 8.7 hours. Assume normality.
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 a Chevrolet Cavalier is randomly selected, find the probability that its rebuild time exceeds 8.7 hours. Assume normality.
Explanation / Answer
Mean = 8.4 hours
Standard deviation = 1.8 hours
P(X < A) = P(Z < (A - mean)/standard deviation)
P(rebuild times exceed 8.7 hours) = P(X > 8.7)
= 1 - P(X < 8.7)
= 1 - P(Z < (8.7 - 8.4)/1.8)
= 1 - P(Z < 0.17)
= 1 - 0.5675 (from standard normal distribution table)
= 0.4325
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