Unformatted text preview: X ∼ N (10 , 4 2 ) and Y ∼ N (15 , 3 2 ), independently. Using moment generating functions (not the theorems), ﬁnd the distribution of W = 2 X + 0 . 5 Y . 5. Suppose heights in a large population are approximately normally distributed with a mean of 5 feet 10 inches and a SD of 2 inches. Suppose a group of 100 people is picked at random from this population. (a) What is the probability that the tallest person in this group is over 6 foot 4 inches tall? (b) What is the probability that the average height of people in the group is over 5 feet 10.5 inches? (c) Suppose instead that the distribution of heights in the population was not normally distributed, but come from some other distribution with the given mean and SD. To which of the problems a). (tallest) and b). (average) would the answer still be approximately the same? Explain carefully....
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 Spring '10
 JO.H
 Math, Normal Distribution, Probability, Probability theory, shut down, Jo Hardin, ﬁrst such snowstorm, Suppose heights

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