Question

Determine if the finite correction factor should be used If so. use it your calculations when you find the probability. In a sample of 900 gas stations the mean price for regular gasoline at the pump was $2.806 per gallon and the standard deviation was $0.009 per gallon A random sample of size 50 is drawn from this population What is the probably that the mean price per gallon is less than $2.803? The probability that the mean price per gallon is less than $2.803 is

Answer 1

To answer the student's question, it is not necessary to use the finite population correction factor for a sample size of 50 out of 900 gas stations. The probability that the mean price is less than $2.803 can be found using the z-score of the sample mean from the standard normal distribution.

Step-by-step explanation:

The student is dealing with a concept in statistics known as the sampling distribution of the sample mean. To find the probability that the mean price per gallon is less than $2.803 when the population mean is $2.806 and the standard deviation is $0.009 for a sample size of 50, we must first check if the finite correction factor should be used. However, the sample size is much smaller than 5% of the population (which has 900 gas stations), so the finite population correction factor is not required.

We can then proceed to use the z-score formula for the sample mean:
z = (x - μ) / (σ / √n), where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Substituting our values we get:
z = (2.803 - 2.806) / (0.009 / √50), and after calculations, this yields a z-score. We then use the z-score to find the corresponding probability from the standard normal distribution table (z-table). This gives us the probability that the sample mean is less than $2.803.