Name: ____________________________ Section: _______________________ Extra Credit – HOMEWORK 5.1 A gasoline tank for a certain car is designed to hold 15 gallons of gas. Suppose that the actual capacity of a randomly selected tank has a distribution that is approximately normal with a mean of 15.0 gallons and a standard deviation of 0.15 gallons. (USE FOR PROBLEMS 1-4) Problem 1: The manufacture of this gasoline tank considers the largest 2% of these tanks too large to put on the market. How large does a tank have to be, to be considered too large? HINT: USE INVNORM : Area to the left will be 1 - .02 Problem 2: What proportion of tanks will hold between 14.75 and 15.10 gallons of gas? Problem 3: If a simple random sample of four tanks is selected, and their capacities can be considered independent, what is the probability that all four will hold between 14.75 and 15.10 gallons of gas? Hint: Use Binomial Distribution with X = 4 Problem 4: If four tanks are randomly selected, what is the probability that their average capacity will be between 14.75 and 15.10 gallons? Problem 5: Chocolate bars produced by a certain machine labeled 8.0 oz. The distribution of the actual weights of these chocolate bars is claimed to be normal with a mean of 8.1 oz and a standard deviation 0.1 oz The quality control manager plans to take a simple random sample of size from the n production line. How big should be so that the sampling distribution of xbar has n standard deviation 0.01 oz?
Name: ____________________________ Section: _______________________ Extra Credit – HOMEWORK 5.1 A gasoline tank for a certain car is designed to hold 15 gallons of gas. Suppose that the actual capacity of a randomly selected tank has a distribution that is approximately normal with a mean of 15.0 gallons and a standard deviation of 0.15 gallons. (USE FOR PROBLEMS 1-4) Problem 1: The manufacture of this gasoline tank considers the largest 2% of these tanks too large to put on the market. How large does a tank have to be, to be considered too large? HINT: USE INVNORM : Area to the left will be 1 - .02 Problem 2: What proportion of tanks will hold between 14.75 and 15.10 gallons of gas? Problem 3: If a simple random sample of four tanks is selected, and their capacities can be considered independent, what is the probability that all four will hold between 14.75 and 15.10 gallons of gas? Hint: Use Binomial Distribution with X = 4 Problem 4: If four tanks are randomly selected, what is the probability that their average capacity will be between 14.75 and 15.10 gallons? Problem 5: Chocolate bars produced by a certain machine labeled 8.0 oz. The distribution of the actual weights of these chocolate bars is claimed to be normal with a mean of 8.1 oz and a standard deviation 0.1 oz The quality control manager plans to take a simple random sample of size n from the production line. How big should n be so that the sampling distribution of xbar has standard deviation 0.01 oz?
5.1_extra_credit.docx