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 800 gas​ stations, the mean price for regular gasoline at the pump was $ 2.849 per gallon and the standard deviation was ​$0.008 per gallon. A random sample of size 50 is drawn from this population. What is the probability that the mean price per gallon is less than ​$2.847​?

The probability that the mean price per gallon is less than ​$2.847 is
nothing.
​(Round to four decimal places as​ needed.)

Answer 1

What is the probability that the mean price per gallon is less than ​$2.847​?

So the answer is 0.0384.

Answer 2

To determine if a finite correction factor should be used, we need to check if the sample size is less than 5% of the population size.

Since the population size is not given, we can assume that it is much larger than the sample size of 50. Therefore, we can use the finite correction factor.

The finite correction factor is given by:

f = sqrt[(N-n)/(N-1)]

where N is the population size and n is the sample size.

Assuming that the population size is much larger than the sample size, we can use:

f = sqrt[(N-n)/(N-1)] ≈ sqrt(0.994) ≈ 0.997

Using the finite correction factor, the standard error of the mean is:

SE = (0.008) / sqrt(50) * 0.997 ≈ 0.00113

To find the probability that the mean price per gallon is less than $2.847, we need to standardize the sample mean:

z = (2.847 - 2.849) / 0.00113 ≈ -1.77

Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score less than -1.77 is approximately 0.0384.

Therefore, the probability that the mean price per gallon is less than $2.847 is 0.0384, or 3.84% (rounded to four decimal places).