Question 5

The number of pages printed before replacing the cartridge in a laser printer is normally distributed with

a mean of 11,500 pages and a standard deviation of 800 pages. A new cartridge has just been installed.

a. What is the probability that the printer produces more than 12,000 pages before this cartridge must

be replaced? [5m]

b. What is the probability that the printer produces fewer than 10,000 pages? [5m]

Question 6 A researcher claims that the average cost of mens athletic shoes is less than $80. He selects a random sample of 36 pairs of shoes from a catalog and finds the following costs (in dollars). He would like to test if there is sufficient evidence to support his claim. 60 70 75 55 80 55 50 40 80 70 50 95 120 90 75 85 80 60 110 65 80 85 85 45 75 60 90 90 60 95 110 85 45 90 70 70 a. Write the null and alternative hypotheses. [2 m] b. Is there enough evidence statistically to support the researchers claim at =0.10? Assume the standard deviation is 19.2. [10 m]