Stat 319: Statistics for Engineering
FORM A
Quiz # 3, 4/ 11 /2006, Instructor: Prof. Hassen A. Muttlak
Name:
ID#
Section
1. (5 points) A mail-order computer business has five telephone lines. Let X denote the number
of lines in use at a specified time. Suppose the pmf of X is as given in the accompanying
table.
x
P(x)
0
0.1
1
0.15
2
0.20
3
0.25
4
0.22
5
0.08
Calculate the probability of each of the following events in part a and b below.
a. {at most 1 lines are in use}
b. {at least 2 lines are in use}
c. Calculate the mean and standard deviation for the number of lines in use.
d. Find E (2X2 + 4X – 10).
2.
(2 points). Each of 12 refrigerators of a certain type has been returned to a distributor because
of the presence of a high-pitched oscillating noise when the refrigerator is running. Suppose
that 5 of these 12 have defective compressors and the other 7 have less serious problems. If
they are examined in random order, let X = the number among the first 6 examined that have
a defective compressor. Compute the probability that at most two refrigerators are defective
among the first 6 examined.
3.
(3 points ) Suppose the average number of accidents happened per a week in a city is 7.
a. What is the probability that exactly 5 accidents will occur in the coming week. 
b. What is the probability that at least 2 accidents will occur in the coming 3 days. 
c. What is the mean and variance of the number of accidents occur in the coming two weeks.
Stat 319: Statistics for Engineering
FORM B
Quiz # 3, 4/ 11 /2006, Instructor: Prof. Hassen A. Muttlak
Name:
ID#
Section
1. (5 points) A mail-order computer business has five telephone lines. Let X denote the number
of lines in use at a specified time. Suppose the pmf of X is as given in the accompanying
table.
x
P(x)
0
0.15
1
0.10
2
0.25
3
0.20
4
0.22
5
0.08
Calculate the probability of each of the following events in part a and b below.
a. {at most 1 lines are in use}
b. {at least 3 lines are in use}
c. Calculate the mean and standard deviation for the number of lines in use.
d. Find E (2X2 + 4X – 10).
2. (2 points). Each of 10 refrigerators of a certain type has been returned to a distributor because
of the presence of a high-pitched oscillating noise when the refrigerator is running. Suppose
that 4 of these 10 have defective compressors and the other 6 have less serious problems. If
they are examined in random order, let X = the number among the first 5 examined that have
a defective compressor. Compute the probability that at most two refrigerators are defective
among the first 5 examined.
3. (3 points ) Suppose the average number of accidents happened per week in a city is 7.
a. What is the probability that exactly 4 accidents will occur in the coming week. 
b. What is the probability that at least 2 accidents will occur in the coming 2 days. 
c. What is the mean and variance of the number of accidents occur in the coming three weeks.