Click here to open the distribution applet Beanie owns a gas pump that is honest

Question

Click here to open the distribution applet Beanie owns a gas pump that is honest. When the pump reads 5 gallons of gas, you might not get exactly 5 gallons because of random variation, but on average it delivers 5 gallons. The standard deviation is 0.5 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 "5 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 0.14 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? Type in "cannot do" if that is your answer

Explanation / Answer

hence probability that pump is ok =

probability that they will declare the pump faulty =1-P(pump ok) =1-0.95 =0.05

for normal distribution z score =(X-)/ here mean=       = 5.000 std deviation   == 0.50 sample size       =n= 49 std error=x=/n= 0.0714

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