Question

Question 1
A small manufacturing company recently instituted Six Sigma training for its employees. Two
methods of training were offered: online and traditional classroom. Management was interested
in whether the division in which employees worked affected their choice of method.

Below is a table summarizing the data.

	Sales	Quality	Operations	Total
Traditional	16	10	8	34
Online	35	23	44	104
Total	51	33	52	136

(a) What is the probability that an employee chose online training? [2 marks]
(b) What is the probability that an employee is in the quality division and chose online training?
[2 marks]
(c) What is the probability that an employee chose online training given that he or she is in the
sales division? [2 marks]
(d) What is the probability that an employee chose online training or is from the sales division?
[3 marks]
(e) Are the events “chose online training” and “from the sales division” independent? Give
reason for your answer. [2 marks]

Question 2
A game consists of flipping a fair coin twice and counting the number of heads that appear. The
distribution for the number of heads, X, is given by: P(X = 0) = ¼; P(X =1) =1/2; P(X = 2) =¼

A player receives $0 for no heads, $2 for 1 head, and $5 for 2 heads (there is no cost to play the
game). Calculate the expected amount of winnings ($). [2 marks]

Question 3
Internet service providers (ISP) need to resolve customer problems as quickly as possible. For
one ISP, past data indicate that the likelihood is 0.80 that customer calls regarding Internet
service interruptions are resolved within one hour. Out of the next 10 customer calls about
interrupted service,
(a) What is the probability that at least 7 will be resolved within one hour? [4 marks]
(b) How many customers would be expected to have their service problems resolved within one
hour? [1 mark]

Question 4
A mail-order company receives an average of five orders per 500 solicitations. If it sends out 100
advertisements, find the probability of receiving at least two orders. [Hint: Use the Poisson
distribution]. Ensure that you define the variable of interest.

Question 5
An airline knows from experience that the distribution of the number of suitcases that get lost
each week on a certain route is approximately normal with μ = 15.5 and σ = 3.6. What is the
probability that during a given week the airline will lose between 10 and 20 suitcases?

Question 6
Assume that the heights of women are normally distributed with a mean of 62.2 inches and a
standard deviation of 2.3 inches. Find the third quartile that separates the bottom 75% from the
top 25%. Total 4 marks

Answer 1