1.The fill amount of bottles of a soft drink is normally distributed, with a mean of 2.0 liters and a standard deviation of 0.05 liter. If you select a random sample of 25 bottles,what is the probability that the sample mean will be

a. between 1.99 and 2.0 liters?

b. below 1.98 liters?

c. greater than 2.01 liters?

d. The probability is 99% that the sample mean amount of soft drink will be at least how much?

e. The probability is 99% that the sample mean amount of soft drink will be between which two values (symmetrically distributed around the mean)?

2. The manufacturer of Ice Melt claims that its product will melt snow and ice at temperatures as low as Fahrenheit .A representative for a large chain of hardware stores is interested in testing this claim. The chain purchases a large shipment of 5-pound bags for distribution. The representative wants to know, with 95% confidence and within what proportion of bags of Ice Melt perform the job as claimed by the manufacturer.

a. How many bags does the representative need to test?What assumption should be made concerning the population proportion? (This is called destructive testing; i.e.,the product being tested is destroyed by the test and isthen unavailable to be sold.)

b. Suppose that the representative tests 50 bags, and 42 ofthem do the job as claimed. Construct a 95% confidence interval estimate for the population proportion that willdo the job as claimed

.c. How can the representative use the results of (b) to determine whether to sell the Ice Melt product?