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 $2.7012.701 per gallon. A random sample of 3838 gas stations is drawn from this population.What is the probability that the mean price for the sample was between $2.6832.683 and $2.7162.716 that week? Assume sigmaequals=$0.0450.045. The probability that the sample mean was between $2.6832.683 and $2.7162.716 is nothing. (Round to four decimal places as needed.) Interpret the results. Choose the correct answer below. A. About 33% of the population of 3838 gas stations that week will have a mean price between$ 2.683$2.683 and $2.7162.716. B. About 9797% of the population of 3838 gas stations that week will have a mean price between$ 2.683$2.683 and $2.7162.716. C. About 33% of samples of 3838 gas stations that week will have a mean price between$ 2.683$2.683 and $2.7162.716. D. About 9797% of samples of 3838 gas stations that week will have a mean price between$ 2.683$2.683 and $2.7162.716.

Explanation / Answer

Ans:

Given that

=0.045

sample size=38

standard error of mean=0.045/sqrt(38)=0.0073

When, sample mean=2.683

z=(2.683-2.701)/0.0073=-2.47

When, sample mean=2.716

z=(2.716-2.701)/0.0073=2.05

P(-2.47<=z<=2.05)=P(z<=2.05)-P(z<=-2.47)

=0.9798-0.0068

=0.9731

About 97% of the population of 38 gas stations that week will have a mean price between 2.683 and 2.716

Option B is correct.

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