, BUSI 230 — WEEK 7 PRACTICE EXAM
Introduction to Probability and Statistics | Liberty University 100
Original Questions with Answers and Rationales | 2026/2027
1. At a store, a normally distributed measurement has mean 70 and standard deviation 8. What is the z-
score of an observation of 82?
A) -1.50
B) 1.50
C) 0.75
D) 0.17
Correct Answer: B) 1.50
Rationale: Standardize using z = (x − µ)/σ = (82 − 70)/8 = 1.50. The sign identifies whether the value is above or below the
mean; dividing by the mean or doubling the standard deviation would use the wrong scale. The interpretation follows the
stated model and its assumptions, not an unsupported assumption about the observed sample.
2. At a clinic, a normally distributed measurement has mean 120 and standard deviation 15. What is the z-
score of an observation of 105?
A) 1.00
B) -1.00
C) -0.50
D) -0.12
Correct Answer: B) -1.00
Rationale: Standardize using z = (x − µ)/σ = (105 − 120)/15 = -1.00. The sign identifies whether the value is above or below
the mean; dividing by the mean or doubling the standard deviation would use the wrong scale. The interpretation follows the
stated model and its assumptions, not an unsupported assumption about the observed sample.
3. At a warehouse, a normally distributed measurement has mean 48 and standard deviation 6. What is
the z-score of an observation of 60?
A) 2.00
B) -2.00
C) 1.00
D) 0.25
Correct Answer: A) 2.00
Rationale: Standardize using z = (x − µ)/σ = (60 − 48)/6 = 2.00. The sign identifies whether the value is above or below the
mean; dividing by the mean or doubling the standard deviation would use the wrong scale. The interpretation follows the
stated model and its assumptions, not an unsupported assumption about the observed sample.
4. At a factory, a normally distributed measurement has mean 250 and standard deviation 20. What is the
z-score of an observation of 230?
BUSI 230 | Independent Practice Examination | 1
, A) -1.00
B) 1.00
C) -0.50
D) -0.08
Correct Answer: A) -1.00
Rationale: Standardize using z = (x − µ)/σ = (230 − 250)/20 = -1.00. The sign identifies whether the value is above or below
the mean; dividing by the mean or doubling the standard deviation would use the wrong scale. The interpretation follows the
stated model and its assumptions, not an unsupported assumption about the observed sample.
5. At a delivery service, a normally distributed measurement has mean 32 and standard deviation 4.
What is the z-score of an observation of 38?
A) -1.50
B) 0.75
C) 0.19
D) 1.50
Correct Answer: D) 1.50
Rationale: Standardize using z = (x − µ)/σ = (38 − 32)/4 = 1.50. The sign identifies whether the value is above or below the
mean; dividing by the mean or doubling the standard deviation would use the wrong scale. The interpretation follows the
stated model and its assumptions, not an unsupported assumption about the observed sample.
6. For a standard normal random variable Z, calculate P(Z < -1.50).
A) 0.9332
B) 0.0668
C) 0.0334
D) 0.1368
Correct Answer: B) 0.0668
Rationale: The standard normal cumulative distribution function gives Φ(-1.50) = 0.0668. The upper-tail complement is 1 −
Φ(z), while halving a cumulative probability has no basis in this question. The interpretation follows the stated model and its
assumptions, not an unsupported assumption about the observed sample.
7. For a standard normal random variable Z, calculate P(Z < -0.80).
A) 0.7881
B) 0.1059
C) 0.2819
D) 0.2119
Correct Answer: D) 0.2119
Rationale: The standard normal cumulative distribution function gives Φ(-0.80) = 0.2119. The upper-tail complement is 1 −
Φ(z), while halving a cumulative probability has no basis in this question. The interpretation follows the stated model and its
assumptions, not an unsupported assumption about the observed sample.
8. For a standard normal random variable Z, calculate P(Z < 0.60).
BUSI 230 | Independent Practice Examination | 2
Introduction to Probability and Statistics | Liberty University 100
Original Questions with Answers and Rationales | 2026/2027
1. At a store, a normally distributed measurement has mean 70 and standard deviation 8. What is the z-
score of an observation of 82?
A) -1.50
B) 1.50
C) 0.75
D) 0.17
Correct Answer: B) 1.50
Rationale: Standardize using z = (x − µ)/σ = (82 − 70)/8 = 1.50. The sign identifies whether the value is above or below the
mean; dividing by the mean or doubling the standard deviation would use the wrong scale. The interpretation follows the
stated model and its assumptions, not an unsupported assumption about the observed sample.
2. At a clinic, a normally distributed measurement has mean 120 and standard deviation 15. What is the z-
score of an observation of 105?
A) 1.00
B) -1.00
C) -0.50
D) -0.12
Correct Answer: B) -1.00
Rationale: Standardize using z = (x − µ)/σ = (105 − 120)/15 = -1.00. The sign identifies whether the value is above or below
the mean; dividing by the mean or doubling the standard deviation would use the wrong scale. The interpretation follows the
stated model and its assumptions, not an unsupported assumption about the observed sample.
3. At a warehouse, a normally distributed measurement has mean 48 and standard deviation 6. What is
the z-score of an observation of 60?
A) 2.00
B) -2.00
C) 1.00
D) 0.25
Correct Answer: A) 2.00
Rationale: Standardize using z = (x − µ)/σ = (60 − 48)/6 = 2.00. The sign identifies whether the value is above or below the
mean; dividing by the mean or doubling the standard deviation would use the wrong scale. The interpretation follows the
stated model and its assumptions, not an unsupported assumption about the observed sample.
4. At a factory, a normally distributed measurement has mean 250 and standard deviation 20. What is the
z-score of an observation of 230?
BUSI 230 | Independent Practice Examination | 1
, A) -1.00
B) 1.00
C) -0.50
D) -0.08
Correct Answer: A) -1.00
Rationale: Standardize using z = (x − µ)/σ = (230 − 250)/20 = -1.00. The sign identifies whether the value is above or below
the mean; dividing by the mean or doubling the standard deviation would use the wrong scale. The interpretation follows the
stated model and its assumptions, not an unsupported assumption about the observed sample.
5. At a delivery service, a normally distributed measurement has mean 32 and standard deviation 4.
What is the z-score of an observation of 38?
A) -1.50
B) 0.75
C) 0.19
D) 1.50
Correct Answer: D) 1.50
Rationale: Standardize using z = (x − µ)/σ = (38 − 32)/4 = 1.50. The sign identifies whether the value is above or below the
mean; dividing by the mean or doubling the standard deviation would use the wrong scale. The interpretation follows the
stated model and its assumptions, not an unsupported assumption about the observed sample.
6. For a standard normal random variable Z, calculate P(Z < -1.50).
A) 0.9332
B) 0.0668
C) 0.0334
D) 0.1368
Correct Answer: B) 0.0668
Rationale: The standard normal cumulative distribution function gives Φ(-1.50) = 0.0668. The upper-tail complement is 1 −
Φ(z), while halving a cumulative probability has no basis in this question. The interpretation follows the stated model and its
assumptions, not an unsupported assumption about the observed sample.
7. For a standard normal random variable Z, calculate P(Z < -0.80).
A) 0.7881
B) 0.1059
C) 0.2819
D) 0.2119
Correct Answer: D) 0.2119
Rationale: The standard normal cumulative distribution function gives Φ(-0.80) = 0.2119. The upper-tail complement is 1 −
Φ(z), while halving a cumulative probability has no basis in this question. The interpretation follows the stated model and its
assumptions, not an unsupported assumption about the observed sample.
8. For a standard normal random variable Z, calculate P(Z < 0.60).
BUSI 230 | Independent Practice Examination | 2
