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?

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JeanaShupp JeanaShupp · Answer 1 · 2019-07-15T06:56:38+02:00

Answer: 0.9932

Step-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 = 55

For 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 .