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Get Full Access to Probability And Statistics For Engineers And The Scientists - 9 Edition - Chapter 3 - Problem 72e
Get Full Access to Probability And Statistics For Engineers And The Scientists - 9 Edition - Chapter 3 - Problem 72e

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A personnel director interviewing 11 senior engineers for

ISBN: 9780321629111 32

Solution for problem 72E Chapter 3

Probability and Statistics for Engineers and the Scientists | 9th Edition

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Problem 72E

A personnel director interviewing 11 senior engineers for four job openings has scheduled six interviews for the first day and five for the second day of interviewing. Assume that the candidates are interviewed in random order. a. What is the probability that x of the top four candidates are interviewed on the first day? b. ?How many of the top four candidates can be expected to be interviewed on the first day?

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Answer: Step1: Given, a personnel director interviewing 11 senior engineers for four job openings has scheduled six interviews for the first day and five for the second day of interviewing. Assume that the candidates are interviewed in random order. Here, N = 11, M = 4, n = 6, N - M = 7. Step2: a). To find the probability that ‘x’ of the top four candidates are interviewed on the first day. X = number of top four candidates are interviewed on the first day. (x )( NM) P(X = x) = Nn x ( n) 4 114 P(X = x) = (x)( 6 x , x = 0,1,2,3,4. (6) Substitute, x = 0,1,2,3,4 in the above equation. 4 114 ( 0( 6 0 P(X = 0) = ( 61 1×7 = 462 P(X = 0) = 0.0151 4 114 (1)( 6 1 P(X = 1) = ( ) 6 4×21 = 462 P(X = 1) = 0.1818 4 114 ( 2( 6 2 P(X = 2) = ( )1 6 = 6×35 462 P(X = 2) = 0.4545 4 114 (3)( 6 3 P(X = 3) = (6) = 4×35 462 = 0.4545 4 114 ( 4( 6 4 P(X = 4) = 11 ( 6 = 1×21 462 = 0.0454 The number of top four candidates are interviewed on the first day are tabulated below x 0 1 2 3 4 p(x) 0.0151 0.1818 0.4545 0.4545 0.0454 Step3: b). To find the top four candidates can be expected to be interviewed on the first day. Mean E(x) = n.( M ) 4 = 6.(11) = 2.1818. Therefore, the top four candidates can be expected to be interviewed on the first day is 2.1818.

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