The average price of a gallon of unleaded regular gasoline was reported to be $2.34 in northern Kentucky (The Cincinnati Enquirer, January 21, 2006). Use this price as the population mean, and assume the population standard deviation is $.20.

a.What is the probability that the mean price for a sample of 30 service stations is within $.03 of the population mean (to 4 decimals)?

b.What is the probability that the mean price for a sample of 50 service stations is within $.03 of the population mean (to 4 decimals)?

Business Week conducted a survey of graduates from 30 top MBA programs (Business Week, September 22, 2003). The survey found that the average annual salary for male and female graduates 10 years after graduation was $168,000 and $117,000, respectively. Assume the population standard deviation for the male graduates is $35,000, and for the female graduates it is $25,000.

a.What is the probability that a simple random sample of 40 male graduates will provide a sample mean within $10,000 of the population mean, $168,000 (to 4 decimals)?

b.What is the probability that a simple random sample of 40 female graduates will provide a sample mean within $10,000 of the population mean, $117,000 (to 4 decimals)?

c.In which of the preceding two cases, part (a) or part (b), do we have a higher probability of obtaining a sample estimate within $10,000 of the population mean?

- Select your answer -Part (a) because the population mean for males is higherPart (a) because the population standard deviation for males is higherPart (b) because the population mean for females is lowerPart (b) because the population standard deviation for females is lower

d.What is the probability that a simple random sample of 100 male graduates will provide a sample mean more than $4,000 below the population mean (to 4 decimals)?

c.What is the probability that the mean price for a sample of 100 service stations is within $.03 of the population mean (to 4 decimals)?

d.Calculate the sample size necessary to guarantee at least .95 probability that the sample mean is within $.03 of the population mean (0 decimals).

a.What is the probability that the mean price for a sample of 30 service stations is within $.03 of the population mean (to 4 decimals)?

b.What is the probability that the mean price for a sample of 50 service stations is within $.03 of the population mean (to 4 decimals)?

Business Week conducted a survey of graduates from 30 top MBA programs (Business Week, September 22, 2003). The survey found that the average annual salary for male and female graduates 10 years after graduation was $168,000 and $117,000, respectively. Assume the population standard deviation for the male graduates is $35,000, and for the female graduates it is $25,000.

a.What is the probability that a simple random sample of 40 male graduates will provide a sample mean within $10,000 of the population mean, $168,000 (to 4 decimals)?

b.What is the probability that a simple random sample of 40 female graduates will provide a sample mean within $10,000 of the population mean, $117,000 (to 4 decimals)?

c.In which of the preceding two cases, part (a) or part (b), do we have a higher probability of obtaining a sample estimate within $10,000 of the population mean?

- Select your answer -Part (a) because the population mean for males is higherPart (a) because the population standard deviation for males is higherPart (b) because the population mean for females is lowerPart (b) because the population standard deviation for females is lower

d.What is the probability that a simple random sample of 100 male graduates will provide a sample mean more than $4,000 below the population mean (to 4 decimals)?

c.What is the probability that the mean price for a sample of 100 service stations is within $.03 of the population mean (to 4 decimals)?

d.Calculate the sample size necessary to guarantee at least .95 probability that the sample mean is within $.03 of the population mean (0 decimals).

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