5. A certain brand of potato chips come in bags labeled with 7 ounces, but the amount in them is not exactly 7 ounces every time. In fact, during the production process, the amount of potato chips the dispensing machine pours into a bag follows a normal distribution with a mean of 7.45 ounces and a standard deviation of 0.25 ounces.

a) What proportion of bags will be filled between 7.20 and 8.05 ounces of chips?

b) A bag holds a max of 8.15 ounces of chips. Every bag that has more than 8.15 ounces of chips poured into it causes a spill and the area needs to be cleaned. What is the probability that the janitor will have to clean a spill?

c) The company wants to guarantee a certain amount of chips to customers so that 96% of bags are filled with more than that amount. What is that amount? Round to two decimal places.

d) Is it unusual for a bag of chips to contain less than 7 ounces? Explain or show work.