Question 1
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 final exam in Math 160 has a mean of 73 with standard deviation 7.73. Assume that a random sample of 24 students is selected and the test score of the sample is computed. Assuming the scores are normally distributed, what percentage of sample means are less than 76?
◦ 97.13%
◦ 66%
◦ 2.87%
◦ 34%
Question 2
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?
◦ 5.48%
◦ 8.08%
◦ 91.92%
◦ 94.52%
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Problem