To estimate the mean height of male students on your campus, you will measure an

Question

To estimate the mean height of male students on your campus, you will measure an SRS of students. Heights of people of the same sex and similar ages are close to Normal. You know from government data that the standard deviation of the heights of young men is about 2.8 inches. Suppose that (unknown to you) the mean height of all male students is 70 inches.

(a) If you choose one student at random, what is the probability that he is between 66 and 68 inches tall?
(b) You measure 36 students. What is the standard deviation of the sampling distribution of their average height x(bar)?
(c) What is the probability that the mean height of your sample is between 66 and 68 inches?

please explain these

Explanation / Answer

ans=

a) Convert to standard normal distribution:

68 ==> (68-70) / 2.8 = -0.714
66 ==> (66 - 70) / 2.8 = -1.4286

The area under the Standard Normal Distribution curve between -1.4286 and 50 is 0.4234
This is also the probability.

b) sigma-sub-x-bar = signal / sqrt(n) = 2.8 / sqrt(36) = 2.8 / 6 = 0.4667

c) This is the same calculation as for (a), but the standard deviation is 0.4667. The answer is 0.5

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