a.Assume that the test scores from a college admissions test are normally distributed with a mean of 450 and a standard deviation of 100.

i.What percentage of the students score below 400

ii. What should be the pass mark if 40% of the students are to pass

b. A manufacturing process has 100 customers' orders to fill. Each order requires one component part that is purchased from a supplier. However typically 2% of the components are identified as defective and components can be assumed to be independent.

If the manufacturer stocks:

100 components, what is the probability that the 100 orders can be filled without

reordering components?

ii.Stocks 102 components, what is the probability that the 100 orders can be filled without reordering components?

c.Past records show that the average number of accidental drowning at a beach resort is 3 per year for every 100,000 of tourists visiting the resort. If in a year 200,000 tourists visited this resort, find the probability that there will be at least two drowning accidents this year