(a) Find the probability that the 4th person weighed is the first person to be overweight. (b) Find the probability that it takes less than 4 people to observe the first overweight person. c) Find the expected value and variance of the number of Americans that would have to be weighed in order to find the first person that was overweight.

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12. A survey conducted discovered that 63% of all Americans are overweight. Suppose that a number of randomly
selected Americans are weighed. The following table may (or may not) be useful:
k 0 1 2 3 4
1 4 6 4 1
4Ck
(a) Find the probability that the 4th person weighed is the first person to be overweight.
(b) Find the probability that it takes less than 4 people to observe the first overweight person.
(c) Find the expected value and variance of the number of Americans that would have to be weighed in
order to find the first person that was overweight.
Transcribed Image Text:12. A survey conducted discovered that 63% of all Americans are overweight. Suppose that a number of randomly selected Americans are weighed. The following table may (or may not) be useful: k 0 1 2 3 4 1 4 6 4 1 4Ck (a) Find the probability that the 4th person weighed is the first person to be overweight. (b) Find the probability that it takes less than 4 people to observe the first overweight person. (c) Find the expected value and variance of the number of Americans that would have to be weighed in order to find the first person that was overweight.
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