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ASSIGNMENT #4
1. A numerical description of the outcome of an experiment is called a
a.
descriptive statistic
b.
probability function
c.
variance
d.
random variable
2. A random variable that can assume only a finite number of values is referred to as a(n)
a.
infinite sequence
b.
finite sequence
c.
discrete random variable
d.
discrete probability function
3. The number of electrical outages in a city varies from day to day. Assume that the number of electrical outages (x) in the city has the following probability distribution.
x
f(x)
0
0.80
1
0.15
2
0.04
3
0.01
The mean and the standard deviation for the number of electrical outages (respectively) are
a.
2.6 and 5.77
b.
0.26 and 0.577
c.
3 and 0.01
d.
0 and 0.8
4. Four percent of the customers of a mortgage company default on their payments. A sample of five customers is selected. What is the probability that exactly two customers in the sample will default on their payments?
a.
0.2592
b.
0.0142
c.
0.9588
d.
0.7408
5. Which of the following is a characteristic of a binomial experiment?
a.
at least 2 outcomes are possible
b.
the probability changes from trial to trial
c.
the trials are independent
d.
none of these alternatives is correct
6. X is a random variable with the probability function:
f(X) = X/6 for X = 1, 2 or 3
The expected value of X is
a.
0.333
b.
0.500
c.
2.000
d.
2.333
7. Roth is a computer-consulting firm. The number of new clients that they have obtained each month has ranged from 0 to 6. The number of new clients has the probability distribution that is shown below.
Number of
New Clients
Probability
0
0.05
1
0.10
2
0.15
3
0.35
4
0.20
5
0.10
6
0.05
The expected number of new clients per month is
a.
6
b.
0
c.
3.05
d.
21
8. Refer to question 7. The variance is
a.
1.431
b.
2.047
c.
3.05
d.
21
9. Refer to question 7. The standard deviation is
a.
1.431
b.
2.047
c.
3.05
d.
21
10. The random variable X is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3.
The expected value of the random variable X is
a.
2
b.
5.3
c.
10
d.
2.30
11. Refer to question 10. The probability that there are 8 occurrences is
a.
0.0241
b.
0.0771
c.
0.1126
d.
0.9107
12. Refer to question 10. The probability that there are less than 3 occurrences is
a.
0.0659
b.
0.0948
c.
0.1016
d.
0.1239
13. An insurance company finds that .003% of the population dies of a certain disease each year. The company has insured 100,000 people against death from this disease. Compute the probability that the firm must pay off in three or more cases next year.
a.
0.6266
b.
0.5768
c.
0.4232
d.
0.9910
14. A local polling organization maintains that 90% of the eligible voters have never heard of John Anderson, who was a presidential candidate in 1980. If this is so, what is the probability that in a randomly selected sample of 12 eligible voters that 2 or fewer have heard of John Anderson?
a.
0.888
b.
0.606
c.
0.112
d.
0.394
15. The probability distribution for the daily sales at Michael's Co. is given below.
Daily Sales
(In $1,000s)
Probability
40
0.1
50
0.4
60
0.3
70
0.2
The expected daily sales are
a.
$55,000
b.
$56,000
c.
$50,000
d.
$70,000
16. Refer to question 15. The probability of having sales of at least $50,000 is
a.
0.5
b.
0.10
c.
0.30
d.
0.90
17. The probability that Pete will catch fish when he goes fishing is .8. Pete is going to fish 3 days next week. Define the random variable X to be the number of days Pete catches fish.
The probability that Pete will catch fish on exactly one day is
a.
0.008
b.
0.096
c.
0.104
d.
0.8
18. Refer to question 17. The probability that Pete will catch fish on one day or less is
a.
0.008
b.
0.096
c.
0.104
d.
0.8
19. Refer to question 17. The expected number of days Pete will catch fish is
a.
0.6
b.
0.8
c.
2.4
d.
3
20. Refer to question 17. The variance of the number of days Pete will catch fish is
a.
0.16
b.
0.48
c.
0.8
d.
2.4
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