1. For each of the following situations, write down (a) the most appropriate graphical display for the data, and (b) identify a statistic that you might be interested in regarding the data.

(i) [2 marks] A survey of a high school class made up of 34 students asked the following question: "How many minutes do you study on a typical weeknight?".

(ii) [2 marks] A hospital staff member studied the waiting times for 680 patients who arrive at the hospital with a request for emergency service. The hospital staff member noted that the distribution is skewed.

(iii) [2 marks] Students in a Statistics class made up of 38 students were asked the main method of transportation to school. Students' answers were: Canada Line/Skytrain, Cycling, Car, Bus, Walk.

2. Parts (a), (b) and (c) are not related, but they are put together as one question because they are all on Normal distributions. Marks are given for the proper presentation of your solution as taught in class and not just for obtaining the correct answer.

(a) The distribution of marks on a recent exam followed a Normal distribution with a mean of 48 marks and a standard deviation of 6 marks.

(i) [2 marks] The passing mark for this exam was set to be 44 marks. If 119 students sat for the exam, approximately how many students failed the exam? Round your answer to the nearest whole number.

(ii) [2 marks] What is the 70th percentile of the distribution of exam scores?

(iii) [2 marks] What is the minimum mark to be in the top 3%? Leave your answer accurate to 2 decimal places.

(b) [2 marks] Basmati rice is sold in bags of 2 kg. To ensure bags are not sold underweight, the machine is set to put a mean weight of 2004 g in each bag. The manufacturer claims that the process works to a standard deviation of 2.1 g. Calculate the percentage of bags manufactured that are underweight. You are to assume the weights are Normally distributed.

(c) [2 marks] The heights of people in the country Lilliput are Normally distributed with a mean of 82 cm and a standard deviation of 7 cm. Fill in the blank showing how you obtain your answer: 69% of people in Lilliput are over __________ cm tall.