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Question: Women constitute 24% of the science and engineering workforce. In a random sample of 500 science and engineering workforce, what is the probability that more than 130 are women? A ) 13.57% B ) 63.57% C ) 86.43% D ) 86.34% Steps to derive 1 The probability of a woman workforce p = 24 100, q = 1 - p = 76 100 . Sample size, n = 500.2 n·p = 500 × 24 100 = 120 > 5 n·q = 500 × 76 100 = 380 > 5 So, the use of normal approximation to the binomial distribution is permissible.3 Mean, μ = n·p = 500 × 24 100 = 1204 Standard Deviation, σ = n ⋅ p ⋅ q = 5 0 0 × 2 4 1 0 0 × 7 6 1 0 0 = 9.555 Write the problem in probability notation: P (x > 130), where x denotes the number of women.6 P (x > 130 + 0.5) = P (x > 130.5) [Rewrite the problem using the continuity correction factors.]7 The corresponding area under the normal curve distribution is shown in the diagram.8 The z value corresponding to x = 130.5 is given by, z = ( x - μ ) σ = ( 1 3 0 . 5 - 1 2 0 ) 9 . 5 5 = 10.5 9.55 = 1.19 The area between z = 0 and z = 1.10 is 0.3643 by referring to the table. So, the area for z > 1.10 is 0.5 - 0.3643 = 0.1357.10 So, the probability that more than 130 are women is 13.57 %.Hence the right answer is Option A Click Here To Go Back Few Other Questions - Solve: 14-y2 + 3 = 5.. Solve: 2+y2 + 6 = 14.. Solve: 93b = 52.. 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