The office of student services at a large western state university maintains information on the study habits of its full-time students. their studies indicate that the mean amount of time undergraduate students study per week is 20 hours. the hours studied follows the normal distribution with a standard deviation of six hours. suppose we select a random sample of 144 current students. what is the probability that the mean of this sample is less than 19.25 hours?

Question

Mathematics

Yair

27 June, 16:35

The office of student services at a large western state university maintains information on the study habits of its full-time students. their studies indicate that the mean amount of time undergraduate students study per week is 20 hours. the hours studied follows the normal distribution with a standard deviation of six hours. suppose we select a random sample of 144 current students. what is the probability that the mean of this sample is less than 19.25 hours?

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Carmen Ramsey · Answer 1

Answer: 45.03%

To find the answer for this problem, you first need to find the z-score for a value of 19.25.

The z-score is the number of standard deviations from the mean.

Here is the work for our z-score:

19.25 - 20 = - 0.75 / 6 = - 0.125

Now, you just have to use a standard normal distribution table and look up the probability for a z-score of - 0.125. I used the average of the probability for z-scores of - 0.12 and - 0.13 to get 45.03%.