Question: Heights. A population consists of 50% men and 50% women. The empirical distribution of heights over the population yields the following statistics:
|
Average
|
Standard deviation
|
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Men's heights
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67 inches
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3 inches
|
|
Women's heights
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63 inches
|
3 inches
|
a) What is the average height over the whole population?
b) What I s the standard deviation of heights over the whole population?
c) Suppose that men's heights are approximately normally distributed, and that women's heights are as well. Calculate the approximate proportion of individuals in the whole population with heights between 63 and 67 inches.
d) Repeat c) assuming instead that heights are normally distributed over the whole population. Explain why the answers are slightly different.
e) Suppose that a man and a woman are picked at random from this population Making assumptions as in c), what is the probability that the men is taller than the woman? [Hint: No integration required]