The daily water consumption for an Ohio community is normally distributed with a mean consumption of 850,125 gallons and a standard deviation of 64,190 gallons. The community water system will experience a noticeable drop in water pressure when the daily water consumption exceeds 934,672 gallons. What is the probability of experiencing such a drop in water pressure?

Question

Mathematics

Jazmin Bean

5 October, 19:38

The daily water consumption for an Ohio community is normally distributed with a mean consumption of 850,125 gallons and a standard deviation of 64,190 gallons. The community water system will experience a noticeable drop in water pressure when the daily water consumption exceeds 934,672 gallons. What is the probability of experiencing such a drop in water pressure?

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Answers (1)

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Kaelyn Allison · Answer 1

The formula for a z score is

z = (x - µ) / σ

z = (984,000 - 750,000) / 80,000 = 2.925

Hence,

p (x > 984,000) = p (z > 2.925) = 1 - p (z ≤ 2.925)

= 1 - 0.9983 = 0.0017