Solve the problem. Round the standard score to the nearest tenth before using the z-score tables. Express your answer as
a percent rounded to hundredths of a percent.
-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 1.77 hours. Assume that a random sample of 40 mechanics is selected and the mean rebuild time of the sample is computed. Assuming the rebuilding times are normally distributed, what percentage of sample means are greater than 8.0 hours?

Question

Quizplus · Accepted Answer

The standard score (z-score) is calculated as (8.0 - 8.4) / (1.77/√40) = -1.43. Using the z-score table, the probability of a z-score being less than -1.43 is approximately 0.0764, so the probability of being greater is 1 - 0.0764 = 0.9236 or 92.36%. Therefore, the percentage of sample means greater than 8.0 hours is approximately 91.92%.

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