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MATH 3070: Worksheet No.3
NAME:
1. An appliance store has the probability distribution for the number of major appliances sold on a
given day (as shown below). Let X be the number of major appliances sold on a given day. Then
answer the following questions.
Outcome
0
1
2
3
4
5
6
7
8
9
10
Probability
0.10
0.15
0.25
0.14
0.09
0.08
0.06
0.05
0.04
0.025
0.015
(a) Construct the graph of probability distribution for the number of major appliances sold on a
given day.
(
X

2
)
(
X

7
)
(
1

X

5
)
(b) Find P
, P
, and P
.
2. The weekly demand for copies of a popular word-processing program at a computer store has the
probability distribution as shown below.
Outcome
0
1
2
3
4
5
6
7
8
9
10
(a)
(b)
(c)
(d)
Probability
0.06
0.14
0.16
0.14
0.12
0.10
0.08
0.07
0.06
0.04
0.03
Construct the graph of probability distribution for the weekly demand.
What is the probability that three or more copies will be needed in a particular week?
What is the probability that the demand will be for at least two but no more than six copies?
It the store has eight copies of the program available at the beginning of each week, what is
the probability the demand will exceed the supply in a given week?
3. An experiment is conducted to test the effect of an anticoagulant drug on rats. The drug
manufacturer claims that 70% of the rats will be favorably affected by the drug. A random sample of
eight rats is employed in the experiment. Answer the following questions:
(a) It is a binomial experiment. Identify the “success” event, the probability of success, and the
number of trials in the experiment.
(b) Construct the graph of probability distribution for the number of rats that will be favorably
affected.
(c) Compute the following probability:
i. At least five experimental rats will be favorably affected.
ii. One or fewer will be favorably affected.
4. In an inspection of automobiles in Los Angeles, 60% of all automobiles had emissions that do not
meet EPA regulations. For a random sample of ten automobiles, complete the following questions:
(a) The data should represent a binomial experiment. Identify the “success” event, the
probability of success, and the number of trials in the experiment.
(b) Construct the graph of probability distribution for the number of automobiles that failed the
inspection.
(c) Compute the following probability:
i. All ten automobiles failed the inspection.
ii. Exactly six of the ten failed the inspection.
iii. Six or more failed the inspection.
iv. All ten passed the inspection.
5. A prescription drug firm claims that only 12% of all new drugs shown to be effective in animal tests
ever make it through a clinical testing program and onto the market. Now suppose that the firm has
15 new compounds that have shown effectiveness in animal tests. Find the following probability:
(a) None reach the market.
(b) One or more reach the market.
(c) Two or more reach the market.