Beanie owns a gas pump that is honest. When the pump reads 17 gallons of gas, yo

Question

Beanie owns a gas pump that is honest. When the pump reads 17 gallons of gas, you might not get exactly 17 gallons because of random variation, but on average it delivers 17 gallons. The standard deviation is 0.3 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 "17 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 0.09 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

Answer to the question)

Mean ( M) = 17

Standard deviation ( s ) = 0.3

Number of trials ( n ) = 49

X1 = 17-0.09 = 16.91

X2 = 17+0.09 = 17.09

.

The formula of Z is as follows:

Z = ( x - M ) / (s / sqrt(n) )

For x1 = 16.91

Z1 = (16.91 -17) / (0.3/sqrt(49))

Z1 = -2.1

P(x<16.91) = 0.01786

.

For x2 = 17.09

Z2 = (17.09-17) / (0.3/sqrt(49))

Z2 = 2.1

P(x<17.09) = 0.9821

.

P(16.91 < x < 17.09) = P(x < 17.09) – P(x < 16.91)

P(16.91 < x < 17.09) = 0.9821 – 0.01786

P(16.91 < x < 17.09) = 0.96424

.

This is the probability of the pump NOT being faulty

The probability of the pump being faulty = 1 – 0.96424 = 0.03576

.

Since the probability of the pump being faulty is 0.03576 which is less than 0.05, hence it is a rare event

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