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# EXAM 1-A - STAT 400 Fall 2011 Version A Name BD1 Th 2:30...

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STAT 400 Fall 2011 Name ANSWERS . Version A BD1 BD2 BD3 BD4 Th 2:30 We 4:00 We 4:00 Th 2:30 317 DKH 165 Noyes 143 Altgeld 328 Armory Srijan Sengupta Srijan Sengupta Robert Eisinger Robert Eisinger Exam 1 Please circle your discussion section. Be sure to show all your work; your partial credit might depend on it. No credit will be given without supporting work. The exam is closed book and closed notes. You are allowed to use a calculator and one 8½" x 11" sheet with notes. Page 1 2 3 4 5 6 7 Total Earned / 70

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1. Alex sells Statistics Made Easy videos over the phone to finance his college education. Suppose 30% of all calls result in a sale. Assume that the outcome of each call is independent of the others. a) (3) What is the probability that Alex makes his first sale on the fourth call? No sale No sale No sale Sale (0.70) (0.70) (0.70) (0.30) = 0.1029 . b) (5) What is the probability that Alex makes his first sale on an even-numbered call? P(even) = P(2) + P(4) + P(6) + … = + + + 5 3 1 70 . 0 0.30 70 . 0 0.30 70 . 0 30 . 0 = 17 7 49 . 0 1 1 21 . 0 49 . 0 21 . 0 70 . 0 21 . 0 0 0 2 = - = = = = n n k k 0.4117647 . OR P(even) = + + + 5 3 1 70 . 0 0.30 70 . 0 0.30 70 . 0 30 . 0 P(odd) = + + + 4 2 0 70 . 0 0.30 70 . 0 0.30 70 . 0 30 . 0 P(even) = 0.70 P(odd), P(odd) = 7 10 P(even). 1 = P(odd) + P(even) = 7 17 P(even). P(even) = 17 7 0.4117647 . c) (3) What is the probability that Alex makes his third sale on the eighth call? [ 7 calls: 2 S’s & 5 F’s ] S ( ) ( ) [ ] 70 . 0 30 . 0 2 7 5 2 C 0.30 0.0953 .
1. (continued) d) (3) If Alex makes 10 calls, what is the probability that he makes exactly 4 sales? Let X = the number of sales made during 10 phone calls. The outcome of each call is independent of the others Binomial distribution, n = 10, p = 0.30. Need P( X = 4) = ? k n k p p k C n k X - - = = ) 1 ( ) P( P( X = 4) = 6 4 ) 70 0 ( ) 30 0 ( 4 10 . . C = 0.20012 . OR Using Cumulative Binomial Probabilities: P( X = 4) = P( X 4) – P( X 3) = CDF @ 4 – CDF @ 3 = 0.850 – 0.650 = 0.200 . e) (3) If Alex makes 10 calls, what is the probability that he makes at least 3 sales?

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