Question

At the gas pump, the metering system is inspected once a month and is under strict standards. Assume you have been hired as one of these inspectors and you are to go to the Walmarts in one city and measure the amount pumped per fuel pump. Your take 40 one gallon samples. Given the average for the pumps is 1 gallon with a standard deviation of .03 gallons, what is the chance the sample average for the Walmart pumps is less than .98 gallons?

Answer 1

Answer: P(x < 0.98) = 0.21

Explanation:

Assuming a normal distribution for the amount of gas pumped per fuel pump, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ/√n

Where

x = amount of gas pumped per fuel pump

µ = mean amount

σ = standard deviation

n = number of sample

From the information given,

µ = 1 gallon

σ = 0.03 gallons

n = 40

The probability that the sample average for the Walmart pumps is less than 0.98 gallons is expressed as

P(x < 0.98)

For x = 0.98

z = (0.98 - 1)/0.03/√40 = - 4.2

Looking at the normal distribution table, the probability corresponding to the z score is 0.21