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.

solution: we have, mean = 8.4 hrs, std. deviation = 1.8 hrs, sample size n = 40, X = 8.9 Probability (X<8.9) = ? we know that, Z = (X - mean) / (std. deviation / (sqrt. n)) = (8.9 - 8.4) / (1.8 / (sqrt. 40)) Z = 1.7568 from standard normal probabilities table, we have, P (Z<1.7568) = 0.9608 Hence, probability that the mean rebuild time is less than 8.9 hours is 0.9608