Phoenix water is provided to approximately 1.4 million people, who are served th
ID: 3056386 • Letter: P
Question
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 0.0016, and 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 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.
Explanation / Answer
Solution:- Given thaat n = 362000 , p = 0.0016 q = 1-p = 1-0.0016 = 0.9984
a) mean = n*p = 362000* 0.0016 = 579.2
standard devition:- sqrt(npq) = sqrt(362000* 0.0016*0.9984) = 24.0473
b) P(X < 350) = P(Z < (X - )/) = P(Z < (350 - 579.2)/24.0473)
= P(Z < -9.5312)
= 0
c) X = (1.645*24.0473)+579.2 = 618.7578 = 619
d) P(X > 400) = P(Z > (400 - 579.2)/24.0473) = P(Z > -7.4520) = 1
by independence,the probability is 1^2 = 1