Question 1

d) A large-scale survey was undertaken on whether someone would buy a product (B), and the following information was found.

50% of those surveyed are male (A),

40% of the males surveyed would buy the product (B | A), and

50% of the females surveyed would buy the product (B | A').

If one of the surveyed is selected at random

i. What is the probability that someone buys the product, P(B)?

A 0.264 B 0.653 C 0.450 D 0.132,

ii What is probability that the buyer of the product is male, P (A | B)?

A 0.472 B 0.630 C 0.528 D 0.444

Question 2:

e) A new shopping mall is considering setting up an information desk manned by one employee. Based upon information obtained from similar information desks, it is believed that people will arrive at the desk on average at a rate of 12 per hour. It is assumed that the arrivals follow a Poisson distribution.

i. What is the probability that there will be more than 14 arrivals at the information desk in an hour?

A 0.6815 B 0.2280 C 0.3185 D 0.7720

ii. If the employee takes a 10-minute break, what is the probability that at least one person will arrive at the information desk?

A 0.8647 B 0.4060 C 0.0000 D 0.5940

Question 3:

f) A company issues a general knowledge test to its potential employees as part of its recruitment procedures. The scores on this test are normally distributed, with a mean of 60 and a standard deviation of 17. If we let x equal the test score, answer the following questions

i. What is the probability that an employee scores less than 50?

A 0.2667 B 0.2776 C 0.7224 D -0.59

ii. What is the probability that an employee scores more than 80?

A 0.1190 B 0.8810 C 0.9772 D 0.2374

iii. The company does not invite the lowest scoring 20% back for a second interview. What mark (to the nearest whole number) must a candidate achieve in order to secure a second interview?

A 45 B 74 C 46 D 75