Phoenix water is provided to approximately 1.4 million people who are served through more than 362,000 accounts (http:// phoenix.gov/WATER/wtrfacts.html). All accounts are metered and billed monthly. The probability that an account has an error in a month is 0.001, and accounts can be assumed to be independent.

(a) What are 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 exceeds this value is 0.05.

(d) Approximate the probability of more than 400 errors per month in the next two months. Assume that results between months are independent.

Solution 100E

Step1 of 5:

Let us consider a random variable X it presents the number of accounts which had an error with parameters n = 362000 and p = 0.001.

Here our goal is:

a). We need to find the mean and standard deviation of the number of account errors each month.

b). We need to find

c). We need to find the value of ‘x’, when

d). We need to find

Step2 of 5:

a).

Let the random variable X follows binomial distribution with parameters ‘n and p.’ and we know that the mean of the binomial distribution is:

Standard deviation of binomial distribution is:

Therefore, mean of X is and standard deviation of X is

Step3 of 5:

b).

Consider,

Where, is obtained from standard normal table(area under normal curve).

(In area under normal curve we have to see in row -0.6 under column 0.04)

Hence,

Therefore,

Step4 of 5:

c).

Let us consider ‘x’ be value, Then consider:

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