1. 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)?
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 probabilities that the sample mean is within $.03 of the population mean (0 decimals).
2. A simple random sample of 40 items resulted in a sample mean of 25. The population standard deviation is 5.
a. What is the standard error of the mean (to 2 decimals)?
b. At 95% confidence, what is the margin of error (to 2 decimals)?
3. In an effort to estimate the mean amount spent per customer for dinner at a major Atlanta restaurant, data were collected for a sample of 49 customers. Assume a population standard deviation of $5.
a. At 95% confidence, what is the margin of error (to 1 decimal)?
b. If the sample mean is $24.80, what is the 95% confidence interval for the population mean (to 1 decimal)?