According to an automobile association, the average cost of a gallon of regular unleaded fuel at gas stations in a certain month was $2.832.

Assume that the standard deviation of such costs is $0.15.

Suppose that a random sample of n=100 gas stations is selected from the population and the month's cost per gallon of regular unleaded fuel is determined for each. Consider x, the sample mean cost per gallon. Complete part a through d.

According to an automobile association, the average cost of a gallon of regular unleaded fuel at gas stations in a certain month was $2.832. Assume that the standard deviation of such costs is $0.15. Suppose that a random sample of n = 100 gas stations is selected from the population and the month's cost per gallon of regular unleaded fuel is determined for each. Consider x, the sample mean cost per gallon. Complete part a through d. Click the icon to view the table of normal curve areas. a. Calculate ux and ox- HX =0 (Do not include the $ symbol in your answer. Round to three decimal places as needed.) (Do not include the $ symbol in your answer. Round to three decimal places as needed.) b. What is the approximate probability that the sample has a mean fuel cost between $2.84 and $2.86? P(2.84 x = 2.86) = (Round to four decimal places as needed.) c. What is the approximate probability that the sample has a mean fuel cost that exceeds $2.855? P(x 2 2.855) = (Round to four decimal places as needed.) d. How would the sampling distribution of x change if the sample size n were doubled from 100 to 200? Choose the correct answer below. O A. Hy doesn't change, a increases by a factor of 2 O B. H; decreases by a factor of v/2, ox doesn't change O C. Hy doesn't change, o decreases by a factor of 2 O D. H; doesn't change, a decreases by a factor of /2 How do your answers to parts b and c change when the sample size is doubled? Choose the correct answer below. O A. P(2.84 x s 2.86) increases, P(x 2 2.855) decreases O B. P(2.84 x s 2.86) decreases, P(x 2 2.855) increases O C. P(2.84 x s 2.86) increases, P(x 2 2.855) increases O D. P(2.84 5x= 2.86) decreases, P(x 2 2.855) decreases\f