Question

Determine if the finite correction factor should be used. If​ so, use it in your calculations when you find the

probability.

In a sample of

700

gas​ stations, the mean price for regular gasoline at the pump was

$ 2.881

per gallon and the standard deviation was

​$0.009

per gallon. A random sample of size

55

is drawn from this population. What is the probability that the mean price per gallon is less than

​$2.879​?

The probability that the mean price per gallon is less than

​$2.879

is

Answer 1

N = Population Size = 700

= Population mean = 2.881

= Population SD = 0.009

n = Sample Size = 55

Finite Population Correction Factor (FPC) is got as follows:

Since calculated value of FPC is not very close to 1, Finite Population Correction is to be done.

With FPC, Standard Error (SE) is got as follows:

To find P(<2.879)

Z = (2.879 - 2.881)/0.001166

= - 1.7156

Table of Area Under Standard Normal Curve gives area = 0.4573

So,

P(<2.879) = 0.5 - 0.4573 = 0.0427

So,

Answer is:

0.0427