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%

Question

Graham Mccarthy

Mathematics

1 January, 21:21

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%

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Answers (1)

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Chaya Boone · Answer 1

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

Step-by-step 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.