FALL 2015
MATH 141 - ASSIGNMENT (8.1-8.3)
DUE: 11/16/15
Name
All steps must be written clearly and neatly to get full credit. If you use your calculator for
anything beyond an arithmetic calculation, please indicate how at the appropriate step.
1. (8pts) Roger Hunt intends to purchase one of two car dealerships currently for sale in a
certain city. Records obtained from each of the two dealers reveal that their weekly volume of
sales, with corresponding probabilities, are as follows:
Dahl Motors:
Cars sold/week 5
6
7
8
9 10 11 12
Probability
.05 .09 .14 .24 .18 .14 .11 .05
Farthington Auto Sales:
Cars sold/week 5
6
7
8
9 10
Probability
.08 .21 .31 .24 .10 .06
The average profit per car at Dahl Motors is $543, and the average profit per car at Farthington Auto Sales is $654.
(i) Find the average number of cars sold each week at each dealership.
Dahl: .05(5) + .09(6) + .14(7) + .24(8) + .18(9) + .14(10) + .11(11) + .05(12) = 8.52
Farthington: .08(5) + .21(6) + .31(7) + .24(8) + .10(9) + .06(10) = 7.25
(or use 1-Var Stats in the calculator)
Remark: Although we’re talking about the number of cars, it is perfectly fine to leave
the average number in decimals. In fact, you will want to use the exact value rather
than the rounded value in the next part.
(ii) If Roger’s objective is to purchase the dealership that generates the higher weekly profit,
which dealership should he purchase?
Dahl: 8.52(543) = $4626.36
Farthington: 7.25(654) = $4741.50
He should choose Farthington.
1
2
ASSIGNMENT (8.1-8.3)
2. (12pts) The market research department of the National Real Estate Company conducted
a survey among 500 prospective buyers in a suburb of a large metropolitan area to determine
the maximum price a prospective buyer would be willing to pay for a house. From the data
collected, the distribution that follows was obtained:
Max. price considered, x 480 490 500 510 520 550 580 600 650
10
20
75
85
70
90
90
55
5
P (X = x)
500
500
500
500
500
500
500
500
500
Compute the mean, median, mode, standard deviation, and variance of the maximum price
x (in thousands of dollars) that these buyers were willing to pay for a house.
The mean and the standard deviation can be obtained by using 1-Var Stats in the calculator.
They are 539.6 and 37.9979 respectively (both in thousands of dollars).
Since there are 500 data points, the median is the average of the 250th and the 251st, both
of which happen to be 520. Thus the median is 520 (thousand dollars).
The modes are 550 and 580 (thousand dollars) since these are the ones that occur most
frequently.
The variance is the square of the standard deviation, so it is 1443.84.
3. (5pts) The odds against an event E occurring are 3 to 5. What is the probability of E not
occurring?
5
Odds in favor of E are 5 to 3, so P (E) = 5+3
= 58 , and P (E c ) = 1 − 58 = 83 .
4. (5pts) The probability of an event not occurring is .7. What are the odds in favor of E
occurring?
(E)
.3
3
P (E c ) = .7 so P (E) = 1 − .7 = .3, and the odds in favor of E are PP(E
c ) = .7 = 7 .