Monthly water bills for a city have a mean of $108.43 and a standard deviation of $32.09. find the probability that a randomly selected bill will have an amount greater than $155, which the city believes might indicate that someone is wasting water. would a bill that size be considered unusual?

The probability that a randomly selected bill will have an amount greater than $155 is 0.07353.    

No, a bill with $155 can not be considered unusual.

Step-by-step explanation:

We have been given that monthly water bills for a city have a mean of $108.43 and a standard deviation of $32.09.

Let us find the z-score for the raw score 155, using z-score formula.

, where,

,

,

,

.

Upon substituting our given values in above formula we will get,

Let us find probability of z-score greater than 1.45.

Using normal distribution table we will get,

Therefore, the probability that a randomly selected bill will have an amount greater than $155 is 0.07353 or approximately 7.35%.    

Since z-scores lower than -1.96 or higher than 1.96 are considered unusual. As the bill with size $155 has z-score of 1.45, therefore, a bill with size $155 can not be considered unusual.

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