INSTRUCTOR ANSWER GUIDE
,CHAPTER 4: DISCRETE RANDOM VARIABLE
Exercise 1. A company wants to evaluate its attrition rate, in other words, how long new hires
stay with the company. Over the years, they have established the following
probability distribution.
Let X = the number of years a new hire will stay with the company.
Let P(x) = the probability that a new hire will stay with the company x years.
Complete Table 4.1 using the data provided.
x P(x)
0 0.12
1 0.18
2 0.30
3 0.15
4
5 0.10
6 0.05
Table 4.1
Solution x P(x)
0 0.12
1 0.18
2 0.30
3 0.15
4 0.10
5 0.10
6 0.05
Table 4.38
Exercise 2. A company wants to evaluate its attrition rate, in other words, how long new hires
2
January 29, 2026
,OpenStax Introductory Business Statistics 2e
Instructor Answer and Solution Guide
Chapter 4: Discrete Random Variable
stay with the company. Over the years, they have established the following
probability distribution.
Let X = the number of years a new hire will stay with the company.
Let P(x) = the probability that a new hire will stay with the company x years.
P(x = 4) =_______
Solution 0.10
Exercise 3. A company wants to evaluate its attrition rate, in other words, how long new hires
stay with the company. Over the years, they have established the following
probability distribution.
Let X = the number of years a new hire will stay with the company.
Let P(x) = the probability that a new hire will stay with the company x years.
P(x ≥ 5) =_______
Solution 0.10 + 0.05 = 0.15
Exercise 4. A company wants to evaluate its attrition rate, in other words, how long new hires
stay with the company. Over the years, they have established the following
probability distribution.
Let X = the number of years a new hire will stay with the company.
Let P(x) = the probability that a new hire will stay with the company x years.
On average, how long would you expect a new hire to stay with the company?
Solution 0 + 0.18 + 0.60 + 0.45 + 0.40 + 0.50 + 0.30 = 2.43 years
Exercise 5. A company wants to evaluate its attrition rate, in other words, how long new hires
stay with the company. Over the years, they have established the following
probability distribution.
Let X = the number of years a new hire will stay with the company.
Let P(x) = the probability that a new hire will stay with the company x years.
What does the column “P(x)” sum to?
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January 29, 2026
, Solution 1
Exercise 6. A baker is deciding how many batches of muffins to make to sell in his bakery. He
wants to make enough to sell every one and no fewer. Through observation, the
baker has established a probability distribution.
x P(x)
1 0.15
2 0.35
3 0.40
4 0.10
Table 4.2
Define the random variable X.
Solution Let X = the number of batches that the baker will sell.
Exercise 7. A baker is deciding how many batches of muffins to make to sell in his bakery. He
wants to make enough to sell every one and no less. Through observation, the baker
has established a probability distribution.
x P(x)
1 0.15
2 0.35
3 0.40
4 0.10
Table 4.2
What is the probability the baker will sell more than one batch? P(x > 1) =_______
Solution 0.35 + 0.40 + 0.10 = 0.85
Exercise 8. A baker is deciding how many batches of muffins to make to sell in his bakery. He
wants to make enough to sell every one and no less. Through observation, the baker
has established a probability distribution.
x P(x)
4
January 29, 2026
,CHAPTER 4: DISCRETE RANDOM VARIABLE
Exercise 1. A company wants to evaluate its attrition rate, in other words, how long new hires
stay with the company. Over the years, they have established the following
probability distribution.
Let X = the number of years a new hire will stay with the company.
Let P(x) = the probability that a new hire will stay with the company x years.
Complete Table 4.1 using the data provided.
x P(x)
0 0.12
1 0.18
2 0.30
3 0.15
4
5 0.10
6 0.05
Table 4.1
Solution x P(x)
0 0.12
1 0.18
2 0.30
3 0.15
4 0.10
5 0.10
6 0.05
Table 4.38
Exercise 2. A company wants to evaluate its attrition rate, in other words, how long new hires
2
January 29, 2026
,OpenStax Introductory Business Statistics 2e
Instructor Answer and Solution Guide
Chapter 4: Discrete Random Variable
stay with the company. Over the years, they have established the following
probability distribution.
Let X = the number of years a new hire will stay with the company.
Let P(x) = the probability that a new hire will stay with the company x years.
P(x = 4) =_______
Solution 0.10
Exercise 3. A company wants to evaluate its attrition rate, in other words, how long new hires
stay with the company. Over the years, they have established the following
probability distribution.
Let X = the number of years a new hire will stay with the company.
Let P(x) = the probability that a new hire will stay with the company x years.
P(x ≥ 5) =_______
Solution 0.10 + 0.05 = 0.15
Exercise 4. A company wants to evaluate its attrition rate, in other words, how long new hires
stay with the company. Over the years, they have established the following
probability distribution.
Let X = the number of years a new hire will stay with the company.
Let P(x) = the probability that a new hire will stay with the company x years.
On average, how long would you expect a new hire to stay with the company?
Solution 0 + 0.18 + 0.60 + 0.45 + 0.40 + 0.50 + 0.30 = 2.43 years
Exercise 5. A company wants to evaluate its attrition rate, in other words, how long new hires
stay with the company. Over the years, they have established the following
probability distribution.
Let X = the number of years a new hire will stay with the company.
Let P(x) = the probability that a new hire will stay with the company x years.
What does the column “P(x)” sum to?
3
January 29, 2026
, Solution 1
Exercise 6. A baker is deciding how many batches of muffins to make to sell in his bakery. He
wants to make enough to sell every one and no fewer. Through observation, the
baker has established a probability distribution.
x P(x)
1 0.15
2 0.35
3 0.40
4 0.10
Table 4.2
Define the random variable X.
Solution Let X = the number of batches that the baker will sell.
Exercise 7. A baker is deciding how many batches of muffins to make to sell in his bakery. He
wants to make enough to sell every one and no less. Through observation, the baker
has established a probability distribution.
x P(x)
1 0.15
2 0.35
3 0.40
4 0.10
Table 4.2
What is the probability the baker will sell more than one batch? P(x > 1) =_______
Solution 0.35 + 0.40 + 0.10 = 0.85
Exercise 8. A baker is deciding how many batches of muffins to make to sell in his bakery. He
wants to make enough to sell every one and no less. Through observation, the baker
has established a probability distribution.
x P(x)
4
January 29, 2026
