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.

(3marks) i.What percentage of the students score below 400

(5marks) 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.

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

The following sums were obtained for sample of 1 0 salesmen on intelligence and their weekly scores (where x is the test score and y is the sales). Ex = 600 E y = 40 E xy = 2530

= 38400 = 174 .

i. Fit a simple linear regression model between X and Y (5 marks) ii. Obtain the standard error of the slope estimate (7 marks) iii. Test the statistical significance of the intercept at 5% level of significance