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elena-14-01-66 [18.8K]
3 years ago
5

The monthly utility bills in a city are normally distributed, with a mean of $100 and a standard deviation of $10. If 300 utilit

y bills are randomly selected from this city, approximately how many of them will be more than $115?
Mathematics
1 answer:
lesantik [10]3 years ago
3 0

First compute the probability that a bill would exceed $115. Let X be the random variable representing the value of a monthly utility bill. Then transforming to the standard normal distribution we have

Z=\dfrac{X-100}{10}

P(X>115)=P\left(Z>\dfrac{115-100}{10}\right)=P(Z>1.5)\approx0.0668

Then out of 300 randomly selected bills, one can expect about 6.68% of them to cost more than $115, or about 20.

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