December 2010 Final Exam Advanced Quantitative Methods – 201-301-RE Page 1 of 3
1. An urn contains 17 balls identical in every respect except color. There are 6 red balls, 8 green balls, and 3 blue balls.
(a) You draw two balls from the urn, but replace the first ball before drawing the second.
Find the probability that the first ball is red and the second ball is green. [2 marks]
(b) Repeat part (a), but do not replace the first ball before drawing the second. [2 marks]
2. A hair salon completed a survey of 360 customers about satisfaction with service and type of customer. A walk-in
customer is one who has seen no ads and not been referred. The other customers either saw a TV ad or were referred
to the salon (but not both). The results follow.
Walk-In TV Ad Referred Total
Not Satisfied 21 9 5 35
Neutral 18 25 37 80
Satisfied 36 43 59 138
Very Satisfied 28 31 48 107
Total 103 108 149 360
Assume the table represents the entire population of customers. Find the probability that a customer is
(a) Not satisfied [2 marks]
(b) Not satisfied and a walk-in [3 marks]
(c) Not satisfied, given referred [3 marks]
(d) Referred [2 marks]
(e) Are the events not satisfied and referred independent? Explain your answer. [2 marks]
3. A computer package comes with two different choices of printers and four different choices of monitors. If a store
wants to display each package combination that is for sale, how many packages must be displayed? [3 marks]
4. In how many ways can the 40 members of a 4H club select a president, a vice-president, a secretary, and a treasurer?
[
3 marks]
5. In how many different ways can a person choose three movies to see in a theater playing 11movies? [3 marks]
6. Of those mountain climbers who attempt Mt. McKinley, only 65% reach the summit. In a random sample of
11mountain climbers who attempt to climb Mt. McKinley, what is the probability of each of the following?
(a) All 11 reach the summit. [2 marks]
(b) At least 9 reach the summit. [3 marks]
7. Sam is a representative who sells large appliances such as refrigerators and stoves. Let x = number of appliances Sam
sells on a given day. Let P(x) = probability that he sells x appliances. For a random sample of 200 days, Sam had the
following sales record.
x 0 1 2 3 4
P(x) 0.045 0.350 0.300 0.180 0.125
Assume the sales record is representative of the population of all sales days.
(a) Compute the probability that x is less than 3. [1 mark]
(b) Compute the expected value of the x distribution. [2 marks]
(c) Compute the standard deviation of the x distribution. [3 marks]
8. A coach found that about 12% of all hockey games end in overtime. Suppose a random sample of 50 hockey games is
observed.
(a) Find the mean
μ
for the number of games ending in overtime. [2 marks]
(b) Find the standard deviation σ for the number of games ending in overtime. [2 marks]
9. Let x be a random variable that represents the length of time it takes a student to write a term paper for Dr. Adam’s
sociology class. After interviewing many students, it was found that x has an approximate normal distribution with
mean
μ
= 6.8 hours and standard deviation σ = 2.1 hours.
(a) Find the probability that a student in this class takes more than 7.5 hours to write a term paper. [3 marks]
(b) Find the probability that for the entire class of 25 students, the average time to write a term paper is more than 7.5
hours. [
3 marks]
