(1). Two companies A and B are offering 70 and 50 products respectively. Company A is offering 40 software products and 30 hardware products. Company B is offering x hardware products and y software products to be determined.

If a product is selected at random, what is the probability that

(a)This product is a hardware product given that is from company B? (in terms of y)

(b)This product is a hardware product given that is from company A?

(C) For what values of y will the probability in part (a) be greater than the probability in part (b)?

(2). The heights of an adult female population are normally distributed with mean 162 cm and standard deviation 7.5cm.

(a) Find the probability that a randomly chosen adult female is taller than 150 cm.

(b) Sarah is a young girl. She visits her doctor and is told she is at the 60th percentile for height. Assuming that Sarah remains at the 60th percentile, estimate her height as an adult. (use table V)

(3). The test Score of a Math class with 800 students are distributed normally with a mean of 75 and a standard deviation of 7.

a) What percentage of a class has a test score between 68 and 82?

b) Approximately how many students have a test score between 61

and 89?

c) What is the probability that a student chosen at random has a

test score between 54 and 75?

d) Approximately how many students have a test score greater

than or equal to 96?