9. Phoenix water is provided to approximately 1.4 million people, who are served

Question

9. Phoenix water is provided to approximately 1.4 million people, who are served through more than 362,000 accounts (http://phoenix.gov/WATER/wtrfacts.htm). All ac- counts are metered and billed monthly. The probability that an account has an error in a month is 0.001; accounts can be assumed to be independent. (a) What is the mean and standard deviation of the number of account errors each month? (b) Approximate the probability of fewer than 350 errors in a month. (c) Approximate a value so that the probability that the number of errors exceeding this value is 0.05.

Explanation / Answer

Binomial distribution probability

a) Mean = n*p = 362000*0.001 = 362
std. dev = sqrt(npq) = sqrt(362000*0.001*0.999) = 19.0168

b) P(X < 350) using excel function, =BINOM.DIST(349, 362000, 0.001,TRUE)
= 0.2571

c) P(X > x) = 0.05
=BINOM.INV(362000, 0.001, 0.95)
=394

The answer is 393 as P(X >= x) gives 394

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