Electrical engineers recognize that high neutral current in computer power syste

Question

Electrical engineers recognize that high neutral current in computer power systems is a potential problem. A recent survey of computer power system load currents at U.S. sites found that 10% of the sites had high neutral current (IEEE Transactions on Industry Applications, July/August. 1990). In a sample of 20 computer power systems selected from the large number of sites in the country, let x be the number with high neutral current.

Electrical engineers recognize that high neutral current in computer power systems is a potential problem. A recent survey of computer power system load currents at J.S. sites found that 10% of the sites had high neutral current (IEEE Transactions on Industry Applications, July/August. 1990). In a sample of 20 computer power systems selected from the large number of sites in the country, let x be the number with high neutral current. Find mean and standard deviation ofx Find the probability that fewer than two computers have found with high neutral current Find the probability that more than five computers have found with high neutral current

Explanation / Answer

p = 0.1

n = 20

a) mean = n * p = 20 * 0.1 = 2

standard deviation = sqrt(n * p * (1 - p)) = sqrt(20 * 0.1 * 0.9) = 1.34

b) P(X = x) = 20Cx * 0.1x * (1 - 0.1)20-x

P(X < 2) = P(X = 0) + P(X = 1)

               = 20C0 * 0.10 * 0.920 + 20C1 * 0.11 * 0.919

               = 0.3917

c) P(X > 5) = 1 - [P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)]

                   = 1 - [20C0 * 0.10 * 0.920 + 20C1 * 0.11 * 0.919 + 20C2 * 0.12 * 0.918 + 20C3 * 0.13 * 0.917 + 20C4 * 0.14 * 0.916 + 20C5 * 0.15 * 0.915 ]

                      = 1 - 0.9887

                      = 1 - 0.0113

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