Page 152 - Probability Demystified

CHAPTER 8 Other Probability Distributions 141

PRACTICE

1. A telemarketing company gets on average 6 orders per 1000 calls. If a
company calls 500 people, find the probability of getting 2 orders.
2. A crime study for a geographic area showed an average of one home
invasion per 40,000 homes. If an area contains 60,000 homes,
find the probability of exactly 3 home invasions.
3. The average number of phone inquiries to a toll-free number for
a computer help line is 6 per hour. Find the probability that for a
specific hour, the company receives 10 calls.
4. A company receives on average 9 calls every time it airs its commer-
cial. Find the probability of getting 20 calls if the commercial is aired
four times a day.
5. A trucking firm experiences breakdowns for its trucks on the average
of 3 per week. Find the probability that for a given week 5 trucks will
experience breakdowns.

ANSWERS

1. The average is 6 orders per 1000 calls, so the average for 500 calls
would be 3 orders. ¼ 3 and x ¼ 2
x
e ð2:7183Þ 3 3 2
¼ 0:224
x! 2!

2. An average of one home invasion for 40,000 homes means that for
60,000 homes, the average would be 1.5 since the ratio 60, 000 ¼ 1:5
40, 000
and x ¼ 3.
x 1:5 3
e ð2:7183Þ ð1:5Þ
¼ 0:126
x! 3!
3. ¼ 6, x ¼ 10

x
e ð2:7183Þ 6 6 10
¼ 0:041
x! 10!
4. ¼ 4 9 ¼ 36 and x ¼ 20
x
e ð2:1783Þ 36 36 20
¼ 0:0013
x! 20!