The heights of North American women can be described by a normalmodel with a mea

Question

The heights of North American women can be described by a normalmodel with a mean of 63.3inches and a standard deviation of 2.2 inches.

Question 2. A random sample of 4 women isselected. What is the probability that the sample mean height x isgreater than 65.4 inches?
2 (use 4 decimal placesin your answer)

Question 3. A random sample of 9 women isselected. What is the probability that the sample mean height x isgreater than 65.4 inches?
3 (use 4 decimal placesin your answer)

Question 4. The Central Limit Theorem wasneeded to answer questions 1, 2, and 3 above.

Explanation / Answer

Given X~Normal (=63.3, =2.2) Question 1. What is the probability that arandomly selected woman is taller than 65.4 inches? P(X>65.4) =P((X-)/ >(65.4-63.3)/2.2) =P(Z>0.95) = 0.1711 (check normal table)

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