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 $ 2.837 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​?

Answer 1

Answer: 0.9932

Step-by-step explanation:

Given : Mean : $\mu=\ 2.837\text{ per gallon }$

Standard deviation : $\sigma = \ 0.009\text{ per gallon}$

a) The formula for z -score :

$z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

Sample size = 55

For x= $2.834​ ,

$z=\dfrac{2.834-2.837}{\dfrac{0.009}{\sqrt{55}}}\approx2.47$

The p-value = $P(z$

$0.9932443\approx0.9932$

Thus, the probability that the mean price per gallon is less than ​$2.834 is approximately 0.9932 .