Question

Monthly water bills for a city have a mean of $108.43 and a standard deviation of $36.98. Find the probability that a randomly selected bill will have an amount greater than $173, which the city believes might indicate that someone is wasting water. Would a bill that size be considered unusual?

Probability is 0.04, which is unusual as it is less than 5%
Probability is 0.04, which is unusual as it is not less than 5%
Probability is 0.04, which is usual as it is not less than 5%
Probability is 0.04, which is usual as it is less than 5%

Answer 1

Probability is 0.04, which is unusual as it is less than 5%

Explanation:

The event is considered to be unusual if the probability of occurrence of that event is less than 5% or 0.05.

We are given that mean and standard deviation are 108.43 and 36.68.

We have to find P(X>173).

P(X>173)=P((x-mean)/sd>(173-108.43)/36.98)

P(X>173)=P(Z>1.75)

P(X>173)=0.5-0.4599

P(X>173)=0.0401.

As the probability is 0.0401 which is less than 0.05, thus a bill with size $173 will be considered unusual.