Dennis Hogan is the supervisor for the Conowingo Hydroelectric Dam. Mr. Hogan knows that the dam’s turbines generate electricity at the peak rate only when at least 1,000,000 gallons of water pass through the dam each day. He also knows, from experience, that the daily flow is normally distributed, with the mean (µ) equal to 850,000 gallons and a standard deviation (σ) of 200,000 gallons. What is the probability that the turbines will generate at peak rate today?
Answers
Given : Dam’s turbines generate electricity at the peak rate only when at least 1,000,000 gallons of water pass through the dam each day.
Daily flow is normally distributed, with the mean (µ) equal to 850,000 gallons and a standard deviation (σ) of 200,000 gallons.
To Find : What is the probability that the turbines will generate at peak rate today?
Solution:
Mean (µ) = 850,000 gallons
standard deviation (σ) = 200,000 gallons
Z score = ( Value - Mean ) /SD
Value = 1,000,000 gallons
Z score = ( 1,000,000 - 850,000 ) /200,000
=> Z score = 150,000 /200,000
=> Z score = 0.75
Z score = 0.75 means 77.34 %
Hence probability at least 1,000,000 gallons of water pass through the dam each day = (100 - 77.34 )/100
= 22.66/100
= 0.2266
probability that the turbines will generate at peak rate today = 0.2266
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