, BUSI 230 — WEEK 6 PRACTICE EXAM
Introduction to Probability and Statistics | Liberty University
100 Original Multiple-Choice Questions with Worked Rationales | 2026/2027 Edition
1. For a small retailer, a normally distributed measurement has mean 80 and standard deviation
10.
What is the z-score of an observation of 70?
A) -1
B) -0.50
C) 0
D) -2
Correct Answer: A) -1
Rationale: Standardize with z = (x − mean)/standard deviation = (70 − 80)/10 = -1. Using the mean instead of the
spread or reversing the subtraction changes the score. A z-score expresses distance from the mean in standard-
deviation units.
2. At a public library, a variable is normal with mean 100 and SD 12. A standardized result is z = 1.
What raw value does it represent?
A) 88
B) 124
C) 112
D) 101
Correct Answer: C) 112
Rationale: Undo standardization: x = mean + z × SD = 100 + (1)(12) = 112. The standard deviation must be multiplied
by z before adding the mean; subtraction instead of addition reverses the direction.
3. For a normal distribution, what fraction of observations lies below a point one SD below the
mean?
A) 0.5000
B) 0.8413
C) 0.1587
D) 0.6827
Correct Answer: C) 0.1587
Rationale: The standard-normal cumulative table gives P(Z ≤ −1) = 0.1587, P(Z ≤ 1) = 0.8413, P(Z ≤ 2) = 0.9772,
and P(Z ≤ −2) = 0.0228. Here the indicated tail and direction select 0.1587; a complementary area answers the
opposite-side question.
4. A hospital scheduling team samples 25 independent observations from a population with SD
10.
What is the standard error of the sample mean?
BUSI 230 | Week 6 Practice Examination | 2026/2027 1
, A) 2
B) 10
C) 0.40
D) 4
Correct Answer: A) 2
Rationale: For independent observations, SE(x■) = σ/√n = 10/√25 = 2. Dividing by n is too aggressive, while using σ
alone ignores averaging. This standard error describes variability among sample means.
5. Two random samples from the same population have sizes 20 and 40. What is the ratio SE(size
20) /SE(size 40) for their sample means?
A) 0.71
B) 2
C) 1.41
D) 0.50
Correct Answer: C) 1.41
Rationale: With common population SD, SE scales as 1/√n. Thus the ratio is √(40/20) = 1.41. The larger sample has
smaller standard error, so the ratio exceeds one.
6. Sample means from a laboratory are based on n = 36, population mean 60, and population SD
18.
Find the z-score of sample mean 63.
A) 0.17
B) 1
C) -1
D) 3
Correct Answer: B) 1
Rationale: For a sample mean, z = (x■ − µ)/(σ/√n) = (63 − 60)/(18/√36) = 1. The denominator is standard error, not
the SD of individual observations.
7. An online marketplace repeatedly selects unbiased random samples of 25 customers.
Thepopulation mean is 100. What is the expected value of the sample mean?
A) 110
B) 4
C) 90
D) 100
Correct Answer: D) 100
Rationale: For a simple random sample with an unbiased mean estimator, E(x■) = µ = 100, regardless of n. Sample
size affects variability, not the expected center. A single realized sample mean need not equal this value.
BUSI 230 | Week 6 Practice Examination | 2026/2027 2
Introduction to Probability and Statistics | Liberty University
100 Original Multiple-Choice Questions with Worked Rationales | 2026/2027 Edition
1. For a small retailer, a normally distributed measurement has mean 80 and standard deviation
10.
What is the z-score of an observation of 70?
A) -1
B) -0.50
C) 0
D) -2
Correct Answer: A) -1
Rationale: Standardize with z = (x − mean)/standard deviation = (70 − 80)/10 = -1. Using the mean instead of the
spread or reversing the subtraction changes the score. A z-score expresses distance from the mean in standard-
deviation units.
2. At a public library, a variable is normal with mean 100 and SD 12. A standardized result is z = 1.
What raw value does it represent?
A) 88
B) 124
C) 112
D) 101
Correct Answer: C) 112
Rationale: Undo standardization: x = mean + z × SD = 100 + (1)(12) = 112. The standard deviation must be multiplied
by z before adding the mean; subtraction instead of addition reverses the direction.
3. For a normal distribution, what fraction of observations lies below a point one SD below the
mean?
A) 0.5000
B) 0.8413
C) 0.1587
D) 0.6827
Correct Answer: C) 0.1587
Rationale: The standard-normal cumulative table gives P(Z ≤ −1) = 0.1587, P(Z ≤ 1) = 0.8413, P(Z ≤ 2) = 0.9772,
and P(Z ≤ −2) = 0.0228. Here the indicated tail and direction select 0.1587; a complementary area answers the
opposite-side question.
4. A hospital scheduling team samples 25 independent observations from a population with SD
10.
What is the standard error of the sample mean?
BUSI 230 | Week 6 Practice Examination | 2026/2027 1
, A) 2
B) 10
C) 0.40
D) 4
Correct Answer: A) 2
Rationale: For independent observations, SE(x■) = σ/√n = 10/√25 = 2. Dividing by n is too aggressive, while using σ
alone ignores averaging. This standard error describes variability among sample means.
5. Two random samples from the same population have sizes 20 and 40. What is the ratio SE(size
20) /SE(size 40) for their sample means?
A) 0.71
B) 2
C) 1.41
D) 0.50
Correct Answer: C) 1.41
Rationale: With common population SD, SE scales as 1/√n. Thus the ratio is √(40/20) = 1.41. The larger sample has
smaller standard error, so the ratio exceeds one.
6. Sample means from a laboratory are based on n = 36, population mean 60, and population SD
18.
Find the z-score of sample mean 63.
A) 0.17
B) 1
C) -1
D) 3
Correct Answer: B) 1
Rationale: For a sample mean, z = (x■ − µ)/(σ/√n) = (63 − 60)/(18/√36) = 1. The denominator is standard error, not
the SD of individual observations.
7. An online marketplace repeatedly selects unbiased random samples of 25 customers.
Thepopulation mean is 100. What is the expected value of the sample mean?
A) 110
B) 4
C) 90
D) 100
Correct Answer: D) 100
Rationale: For a simple random sample with an unbiased mean estimator, E(x■) = µ = 100, regardless of n. Sample
size affects variability, not the expected center. A single realized sample mean need not equal this value.
BUSI 230 | Week 6 Practice Examination | 2026/2027 2
