BSTAT 2305 FINAL SCRIPT 2026 UPDATED
QUESTIONS WITH DETAILED ANSWERS
GRADED A+
⩥ The accompanying relative frequency distribution represents the last
year car sales for the sales force at Kelly's Mega Used Car Center.
Car Sales - Relative Frequency
35 up to 45 - 0.07
45 up to 55 - 0.15
55 up to 65 - 0.31
65 up to 75 - 0.22
75 up to 85 - 0.25
If Kelly's employs 100 salespeople, how many of these salespeople have
sold at least 65 cars in the last year? Answer: 47
(0.22 + 0.25)100 = 47 employees.
⩥ The number of cars sold by a car salesperson during each of the last
25 weeks is the following:
,Number Sold - Frequency
0 - 10
1 - 10
2-5
What is the probability that the salesperson will sell one car during a
week? Answer: 0.40
P(X = 1) = 10/25 = 0.40
⩥ Consider the following discrete probability distribution.
x - P(X = x)
-10 - 0.35
0 - 0.10
10 - 0.15
20 - 0.40
What is the probability that X is less than 5? Answer: 0.45
P(X < 5) = P(X = −10) + P(X = 0) = 0.35 + 0.10 = 0.45
,⩥ The director of graduate admissions is analyzing the relationship
between scores in the GRE and student performance in graduate school,
as measured by a student's GPA. The table below shows a sample of 10
students. Answer: The correlation between GRE and GPA is positive and
strong.
=CORREL(<GRE data>,<GPA data>) = 0.894
⩥ There are 30 Major League Baseball teams in the National League.
Five of these teams will make the playoffs at the end of the season. The
number of unique groups of teams that can make the playoffs is ______.
Answer: 142,506
In Excel, the function used is =COMBIN(30,5) = 142,506
⩥ The number of homes sold by a realtor during a month has the
following probability distribution:
Number Sold - Probability
0 - 0.20
1 - 0.40
2 - 0.40
, What is the standard deviation of the number of homes sold by the
realtor during a month? Answer: 0.75
The standard deviation of the discrete random variable X is calculated as
SD(X)=σ=√σ^2. The variance of the discrete random variable X is
calculated as Var(X) = σ^2 = ∑(xi − μ)^2 P(X = xi).
E(X) = 0 × 0.20 + 1 × 0.40 + 2 × 0.40 = 1.2
Var(X) = (0 − 1.2)^2 × 0.20 + (1 − 1.2)^2 × 0.40 + (2 − 1.2)2 × 0.40 =
0.56
SD(X) = √0.56 = 0.75
⩥ A company is bidding on two projects, A and B. The probability that
the company wins project A is 0.40 and the probability that the company
wins project B is 0.25. Winning project A and winning project B are
independent events. What is the probability that the company does not
win either project? Answer: 0.45
The addition rule is calculated as P(A∪B) = P(A) + P(B − P(A∩B). A
complement rule is P(A) = 1 − P(A^c).
P(A∪B) = 0.40 + 0.25 − 0.1 = 0.55
Neither = 1 − P(A∪B) = 1 − 0.55 = 0.45
QUESTIONS WITH DETAILED ANSWERS
GRADED A+
⩥ The accompanying relative frequency distribution represents the last
year car sales for the sales force at Kelly's Mega Used Car Center.
Car Sales - Relative Frequency
35 up to 45 - 0.07
45 up to 55 - 0.15
55 up to 65 - 0.31
65 up to 75 - 0.22
75 up to 85 - 0.25
If Kelly's employs 100 salespeople, how many of these salespeople have
sold at least 65 cars in the last year? Answer: 47
(0.22 + 0.25)100 = 47 employees.
⩥ The number of cars sold by a car salesperson during each of the last
25 weeks is the following:
,Number Sold - Frequency
0 - 10
1 - 10
2-5
What is the probability that the salesperson will sell one car during a
week? Answer: 0.40
P(X = 1) = 10/25 = 0.40
⩥ Consider the following discrete probability distribution.
x - P(X = x)
-10 - 0.35
0 - 0.10
10 - 0.15
20 - 0.40
What is the probability that X is less than 5? Answer: 0.45
P(X < 5) = P(X = −10) + P(X = 0) = 0.35 + 0.10 = 0.45
,⩥ The director of graduate admissions is analyzing the relationship
between scores in the GRE and student performance in graduate school,
as measured by a student's GPA. The table below shows a sample of 10
students. Answer: The correlation between GRE and GPA is positive and
strong.
=CORREL(<GRE data>,<GPA data>) = 0.894
⩥ There are 30 Major League Baseball teams in the National League.
Five of these teams will make the playoffs at the end of the season. The
number of unique groups of teams that can make the playoffs is ______.
Answer: 142,506
In Excel, the function used is =COMBIN(30,5) = 142,506
⩥ The number of homes sold by a realtor during a month has the
following probability distribution:
Number Sold - Probability
0 - 0.20
1 - 0.40
2 - 0.40
, What is the standard deviation of the number of homes sold by the
realtor during a month? Answer: 0.75
The standard deviation of the discrete random variable X is calculated as
SD(X)=σ=√σ^2. The variance of the discrete random variable X is
calculated as Var(X) = σ^2 = ∑(xi − μ)^2 P(X = xi).
E(X) = 0 × 0.20 + 1 × 0.40 + 2 × 0.40 = 1.2
Var(X) = (0 − 1.2)^2 × 0.20 + (1 − 1.2)^2 × 0.40 + (2 − 1.2)2 × 0.40 =
0.56
SD(X) = √0.56 = 0.75
⩥ A company is bidding on two projects, A and B. The probability that
the company wins project A is 0.40 and the probability that the company
wins project B is 0.25. Winning project A and winning project B are
independent events. What is the probability that the company does not
win either project? Answer: 0.45
The addition rule is calculated as P(A∪B) = P(A) + P(B − P(A∩B). A
complement rule is P(A) = 1 − P(A^c).
P(A∪B) = 0.40 + 0.25 − 0.1 = 0.55
Neither = 1 − P(A∪B) = 1 − 0.55 = 0.45
