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A particular telephone number is used to receive both
Chapter 4, Problem 50E(choose chapter or problem)
A particular telephone number is used to receive both voice calls and fax messages. Suppose that 25% of the incoming calls involve fax messages, and consider a sample of 25 incoming calls. What is the probability that a.? ?At most 6 of the calls involve a fax message? b.? ?Exactly 6 of the calls involve a fax message? c.? ?At least 6 of the calls involve a fax message? d.? ?More than 6 of the calls involve a fax message?
Questions & Answers
QUESTION:
A particular telephone number is used to receive both voice calls and fax messages. Suppose that 25% of the incoming calls involve fax messages, and consider a sample of 25 incoming calls. What is the probability that a.? ?At most 6 of the calls involve a fax message? b.? ?Exactly 6 of the calls involve a fax message? c.? ?At least 6 of the calls involve a fax message? d.? ?More than 6 of the calls involve a fax message?
ANSWER:Answer: Step1: Given, a particular telephone number is used to receive both voice calls and fax messages. Suppose that 25% of the incoming calls involve fax messages, and consider a sample of 25 incoming calls. Here, n = 25 and p = 25% = 0.25 Let x follows binomial distribution with parameters (n,p). i.e, X ~ B(n,p) x P(x;p,n) = (c )x (1 p) n x i = 0 Step2: a). To find the probability that at most 6 of the calls involve a fax message. Let x follows number of calls involving a fax message. 6 25 x 25x P(x 6) = (c ) (x.25) (1 0.25) i =0 = c( )5 (0.25) (