For each of these questions you must provide a diagram indicating the area or the percentile of the relevant distribution for the question. These diagrams can be drawn and photographed with the picture file pasted in the space provided or cut and pasted from Minitab. You will lose marks if you do not provide diagrams. The answer to each question should be clearly stated (ie. do not just give computer output for an answer).
a. The Flaky Bakery is famous for its crusty croissants. The numbers of calories in these croissants are normally distributed with a mean of 300 and a standard deviation of 16 calories.
i. Find the probability that a randomly selected croissant bought at the Flaky Bakery has less than 320 calories.
ii. Find the probability that a randomly selected croissant bought at the Flaky Bakery has between 280 and 290 calories.
iii. The croissants are packaged into boxes of six. Find the probability that the average number of calories in a box of six randomly selected croissants from the Flaky Bakery is more than 310 calories.