Find the probability and interpret the results If convenient

Find the probability and interpret the results. If convenient, use technology to find the probability. During a certain week the mean price of gasoline was $2.716 per gallon. A random sample of 33 gas stations is drawn from this population. What is the probability that the mean price for the sample was between $2.695 and $2.718 that week? Assume a $0.048. Click the icon to view page 1 of the standard normal table. Click the icon to view page 2 of the standard normal table. The probability that the sample mean was between $2.695 and $2.718 is . (Round to four decimal places as needed.) Interpret the results. Choose the correct answer below. A. About 59% of the population of 33 gas stations that week will have a mean price between $2.695 and $2.718. B. About 41% of samples of 33 gas stations that week will have a mean price between $2.695 and $2.718. C. About 59% of samples of 33 gas stations that week will have a mean price between $2.695 and $2.718. D. About 41% of the population of 33 gas stations that week will have a mean price between $2.695 and $2.718.

Solution

To find P(a <= Z <=b) = F(b) - F(a)
P(X < 2.695) = (2.695-2.716)/0.048/ Sqrt ( 33 )
= -0.021/0.0084
= -2.5132
= P ( Z <-2.5132) From Standard Normal Table
= 0.00598
P(X < 2.718) = (2.718-2.716)/0.048/ Sqrt ( 33 )
= 0.002/0.0084 = 0.2394
= P ( Z <0.2394) From Standard Normal Table
= 0.59459
P(2.695 < X < 2.718) = 0.59459-0.00598 = 0.5886                  

58.86% ~ 59% are b/w 2.695 to 2.718

Ans) Option A