Nearly all-commercial industrial facilities have three-phase power systems, espe

Question

Nearly all-commercial industrial facilities have three-phase power systems, especially for motor and heavy machinery loads (see diagram below). With three-phase power systems comes the expectation that if the three-phases have about the same amount of current, then the neutral will have very little current, thus electrical engineers try to balance the loads so equal amounts of current are drawn on each of the three power legs. There are a number of reasons why such load balancing is desirable, but one reason is that it often results in the least current flowing in the neutral conductor. If high currents are measured in the neutral, or at least higher than we expect, problems may result (e.g. overheating & fire). Also, electrical engineers recognize that high neutral current in computer power systems is a potential problem. A survey of computer power system load currents at US sites found that 10% of the sites had high neutral to full-load current ratios. If a random sample of five computer power systems is selected from the large number of sites in the country, what is the probability that at least three will have a high neutral to full-current load ratio?

Explanation / Answer

Use formula

nCr(p)^r(q)^n-r, where, n is the total number of samples, r is the number of succeses and p is the probability of success and q, the probability of failures.

Now, atleast 3 means P(r greater than equal to 3)=P(r=3)+P(r=4)+P(r=5)

Substituting values of r=3,4 and 5; p=0.90 and q=0.10, the required probability is 0.99144.

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