09 Midterm Review-1

A what is the probability that the next customer will

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a) What is the probability that the next customer will purchase a gift? Denote by M and F the event that a customer is a male and female, respectively. Denote by G the event that a customer makes a purchase. The question states that P(G|M)=.60, P(G|F)=.80, and P(F)=.65. We are asked to compute P(G). P(G) = P(G|M)P(M) + P(G|F)P(F)= (.60)(1-.65) + (.80)(.65)=.73 The probability of selling a gift is 73% for this particular gift shop.
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Example 32 For each of the three situations below, argue whether a Binomial, Poisson, or neither distribution is more appropriate. b) Number of customers who visit the gift shop in the next hour. c) Number of female customers who visit the gift shop in the next hour. d) Number of male customers among the first 10 customers who visit the gift shop.
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Example 33 For each of the three situations below, argue whether a Binomial, Poisson, or neither distribution is more appropriate. b) Number of customers who visit the gift shop in the next hour. Poisson distribution. c) Number of female customers who visit the gift shop in the next hour. Poisson distribution. d) Number of male customers among the first 10 customers who visit the gift shop. Binomial distribution.
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Example 34 Phone calls arrive at a rate of 8 per hour to a reservation desk. a) What is the probability that exactly 8 calls arrive in the next hour? b) What is the probability that no calls arrive in the next half an hour? c) What is the probability that at least one call arrives in the next half an hour?
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Example 35 We use Poisson distribution. a) What is the probability that exactly 8 calls arrive in the next hour? Let X denote the number of calls that arrive in the next hour. X has a Poisson distribution with a rate of 8/hr, t=1hr P(X=8)= b) What is the probability that no calls arrive in the next half an hour? P(X=0)= c) What is the probability that at least one call arrives in the next half an hour? We are asked to compute P(X≥1)=1-P(X=0). We computed P(X=0) in part (b), as a result, P(X≥1) = 1- 0.0183 = 0.9817. (8*1) 8 e - 8*1 8! = 0.1396 (8*0.5) 0 e - 8*0.5 0! = 0.0183
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