Probability Distribution (mean & St. dev)
Name____________________________
1. The probability distribution of x, the number of defective tires on a randomly selected automobile checked at a
certain inspection station, is given in the table below.
x
p(x)
0
0.54
1
0.16
2
0.06
3
0.04
4
0.2
a. Calculate the mean value of x.
b. What is the probability that x exceeds its mean value?
c. Calculate the standard deviation of x.
d. What is the probability that the value is within one deviation of the mean?
2. The following probability is the distribution of y = number of broken eggs in a carton.
y
P(y)
0
0.65
1
0.2
2
0.1
3
0.04
4
0.01
a. Calculate and interpret 𝜇𝑦
b. In the long run, for what percentage of cartons is the number of broken eggs less than 𝜇𝑦 ?
c. Why doesn’t 𝜇𝑦 =
(0+1+2+3+4)
5
= 2? Explain.
d. Calculate and interpret 𝜎𝑦 .
e. What percent are within 2 deviation of the mean
3. The following probability distribution represents x = the number of courses for which a randomly selected student
at a certain university is registered:
x
P(x)
1
0.02
2
0.03
3
0.09
4
0.25
5
0.4
6
0.16
7
0.05
a. Calculate the mean and standard deviation of x.
b. What is the probability that x is more than 1 standard deviation below its mean?
c. What is the probability that x is more than 2 standard deviations away from its mean value?
4. A personal computer salesperson working on commission receives a fixed amount for each system sold. Suppose
that for a given month, the probability distribution of x = number of systems sold is given by the table below.
a. What is the mean number of systems sold?
b. Find the variance and standard deviation of x. How would you interpret these?
c. What is the probability that the number of systems sold is within 1 deviation of the mean?
d. What is the probability that the number of systems sold is more than 2 deviations from the mean?
5. A local television station sells 15 sec, 30 sec, and 60 sec advertising spots. Let x denote the length of a randomly
selected commercial appearing on this station, and suppose that the probability distribution of x is given by the
following table:
x
P(x)
15
0.1
30
0.3
60
0.6
a. Find the average length for commercials appearing on this station?
b. If a 15 sec spot sells for $500, a 30 sec spot for $800 and a 60 sec spot for $1000, find the average amount paid
for commercials appearing on this station.