Find the probability and interpret the results. If convenient, use technology to

Question

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 $2.711 per gallon. A random sample of 36 gas stations is drawn from this population. What is the probability that the mean price for the sample was between $2.693 and $2.721 that week? Assume sigma equals$0.048 . LOADING... Click the icon to view page 1 of the standard normal table. LOADING... Click the icon to view page 2 of the standard normal table. The probability that the sample mean was between $2.693 and $2.721 is nothing . (Round to four decimal places as needed.) Interpret the results. Choose the correct answer below. A. About 88 % of samples of 36 gas stations that week will have a mean price between$ 2.693 and $2.721 . B. About 12 % of the population of 36 gas stations that week will have a mean price between$ 2.693 and $2.721 . C. About 88 % of the population of 36 gas stations that week will have a mean price between$ 2.693 and $2.721 . D. About 12 % of samples of 36 gas stations that week will have a mean price between$ 2.693 and $2.721 .

Explanation / Answer

2.721-2.693=2*Z*0.048/6 ,Z=1.55

Gives the probability estimate from the table to be 0.94 .Which means that there is a 88% probability that we get in between them.

probability that the mean doesnt lie in this region=1-0.88=0.12 or 12% probability that the price doesnt lie between them.

Hence There is a 88% probability of samples of 36 gas stations will have its mean betwen the given values

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