Q:

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 $ 2.837 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 ​$2.834​?

Accepted Solution

A:
Answer: 0.9932Step-by-step explanation:Given : Mean : [tex]\mu=\$2.837\text{ per gallon }[/tex]Standard deviation : [tex]\sigma = \$0.009\text{ per gallon}[/tex]a) The formula for z -score :[tex]z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]Sample size = 55For x= $2.834​ , [tex]z=\dfrac{2.834-2.837}{\dfrac{0.009}{\sqrt{55}}}\approx2.47[/tex]The p-value = [tex]P(z<2.47)=[/tex][tex]0.9932443\approx0.9932[/tex]Thus, the probability that the mean price per gallon is less than ​$2.834 is approximately 0.9932 .