What is the probability they will declare the pump faulty?
Beanie owns a gas pump that is honest. When the pump reads 12 gallons of gas, you might not get exactly 12 gallons because of random variation, but on average it delivers 12 gallons. The standard deviation is 0.4 gallons.
The government is going to do a random check on Beanie's gas pump. They will select 81 random times to fill up to where the gas pump says "12 gallons", and then in the lab they will measure it to see exactly how much gas there is. If the amount of gas is off (either too high or too low) by 0.04 gallons on average, they will declare the pump faulty and shut down his gas station.
What is the probability they will declare the pump faulty?
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