Question

Tanker trucks are designed to carry huge quantities of gasoline from refineries to filling stations. A factory that manufactures the tank of the trucks claims to manufacture tanks with a capacity of 8550 gallons of gasoline. The actual capacity of the tanks is normally distributed with mean μ=8544 gallons and standard deviation σ=12 gallons.

Part 3: What is the probability that a sample of size 20 will have a mean between 8538 and 8550 gallons?

Answer 1

Let X be a random variable which follows standard normal distribution with some mean and variance then their probability density function (pdf) is given by

For mean capacity of 8544 gallons and standard deviation of 12, the pdf is written as

We have to calculate the probability that the mean of sample of size 20 lie between 8538 and 8550 which can be written as

Above probability is obtainned by using the standard normal table or considering the fact that N(0,1) is symmetrical in nature .

Therefore the require probability is given by 2*p(0<Z<z1) which is 0.9748. Therefore the probability is 0.9748 for the mean of sample of size 20 lie between 8538 and 8550.