Beanie owns a gas pump that is accurate and fairly precise: when the pump reads

Question

Beanie owns a gas pump that is accurate and fairly precise: when the pump reads 21 gallons of gas, you might not get exactly 21 gallons because of random variation, but on average it does give you 21 gallons of gas. In other words, µ = 21. The true standard deviation ( ) in the volume of gas pumped is 0.4 gallons. The government is going to do a random check on Beanie's gas pump. They will select 49 random times to fill up to where the gas pump says "21 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 0.17 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?

Explanation / Answer

off by 0.17 means that the average amount around 21-0.17 - 20.83

n = 49

std dev = 0.4

t value must be calculated = (x- mean)/(std dev/ sqrt(n))

= (20.83 - 21)/(0.4/sqrt(49)) = -0.17/0.057 = -2.98

degree of freedom = 49-1 = 48

p value wll be taken prob the t table

which comes around to be 0.0022

hence probability = 0.0022

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