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