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Probability

Find the probability and expected value.

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6) In a marketing study, 20 children were to be selected to try a new cran-raspberry flavored chewing gum. If the probability is 0.6 that a randomly selected child will like the gum, what is the probability that
a) exactly 10 will like the gum?
b) at least 14 will like the gum?
7) In a survey of buyer intentions, consumers may be asked to indicate their intentions of purchasing a particular durable good (say, an automobile) within some time period (say, the next six months) by choosing a value on a purchase probability scale. Assuming that ten consumers are interviewed independently, if four give probabilities of 0.2, four of 0.5, and two of 0.6 to the question about the purchase of the automobile in the next six months, find the expected value and the variance of the total number of automobiles that may be sold to such a group? (Hint: Write the total number sold T as the sum of independent binomial or Bernoulli random variables.)
8) A population consisting of 30 items contains 20 items if type A and 10 of type B. If X represents the number of items of type A in a sample of 5 items taken without replacement, find the following:
a) P(X = 3) ,
b) P(X 2) ,
c) E(X) ,

9) Valerie is an auditor who is going to study the checking accounts in a small bank. The bank has 500 accounts, and Valerie plans to sample 5 of these accounts in the first stage of her audit. If one or more of these 5 is found to be in error, she will taken a second (larger) sample. Find the probability she will need to take a second sample if, in fact,
a) 25 of the accounts are actually in error.
b) 50 of the accounts are actually in error.
c) 100 of the accounts are actually in error.
10) If Y is a Poisson random variable with = 3, find
a) P(Y 4) ,
b) P(Y = 2) ,
c) E(Y) ,

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