The most widely used continuous probability distribution in practice is the normal distribution because a large majority of continuous random variables have outcomes that follow a normal pattern. Given a normally distributed population with a mean (μ) of 35, a standard deviation (σ) of 12, and 40 as the number of cases (N), answer the following questions:

i. What is the proportion of cases with a raw score less than 43?(6)

ii. What is the percentage of cases with a raw score greater than 24?(6)

iii. What is the number of cases with raw scores between 30 and 42? (8)

b. A test consists of ten multiple choice questions with four choices for each question. As an experiment, you GUESS on each and every answer without even reading the questions. What is the probability of getting at least seven questions correct on this test?(8)

c. Suppose the average number of customers at a gas station in any 60 minute-period is equal to 12. What is the probability that there will be exactly four or six customers in any 30 minute-period?