FALL 2015
MATH 141 - ASSIGNMENT (7.1-7.3)
DUE: 11/2/15
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) The arrival times of the 8 a.m. Boston-based commuter train as observed in the
suburban town of Sharon over 120 weekdays is summarized below:
Arrival time, x
Frequency of occurrence
7:56 a.m. < x ≤ 7:58 a.m.
4
7:58 a.m. < x ≤ 8:00 a.m.
18
8:00 a.m. < x ≤ 8:02 a.m.
50
8:02 a.m. < x ≤ 8:04 a.m.
32
8:04 a.m. < x ≤ 8:06 a.m.
9
8:06 a.m. < x ≤ 8:08 a.m.
4
8:08 a.m. < x ≤ 8:10 a.m.
3
(i) Find the sample space for this experiment.
{(7 : 56 < x ≤ 7 : 58), (7 : 58 < x ≤ 8 : 00), (8 : 00 < x ≤ 8 : 02), (8 : 02 < x ≤ 8 :
04), (8 : 04 < x ≤ 8 : 06), (8 : 06 < x ≤ 8 : 08), (8 : 08 < x ≤ 8 : 10)}
(If you use letters to represent each of the outcomes, then you should state what each
letter represents.)
(ii) Find the probability distribution for this experiment.
Arrival time, x
Probability
7:56 a.m. < x ≤ 7:58 a.m.
4/120
7:58 a.m. < x ≤ 8:00 a.m.
18/120
8:00 a.m. < x ≤ 8:02 a.m.
50/120
8:02 a.m. < x ≤ 8:04 a.m.
32/120
8:04 a.m. < x ≤ 8:06 a.m.
9/120
8:06 a.m. < x ≤ 8:08 a.m.
4/120
8:08 a.m. < x ≤ 8:10 a.m.
3/120
(iii) What is the probability that the train arrives between 7:58 a.m. and 8:02 a.m.?
18
50
68
17
P (train arrives between 7:58 a.m. and 8:02 a.m.) =
+
=
(= )
120 120
120
30
1
2
ASSIGNMENT (7.1-7.3)
2. (7pts) The probability that a shopper in a certain boutique will buy a blouse is .35, the
probability that she will buy a pair of pants is .30, and the probability that she will buy a skirt
is .27.
The probability that she will buy both a blouse and a skirt is .15, the probability that she
will buy both a skirt and a pair of pants is .19, and the probability that she will buy both a
blouse and a pair of pants is .12. Finally, the probability that she will buy all three items is .08.
What is the probability that a customer selected at random will buy:
(i) Exactly one of these items?
.16+.01+.07=.24
(ii) None of these items?
.46
(Answers were obtained by filling in a Venn diagram with the various probabilities.
The Venn diagram should be included as part of your work.)