CNA Positioning Transfers & Mobility Assistance 2026
Q1: A researcher collects data on the number of cars in a parking lot at 9 AM each day for 30 days.
What type of variable is "number of cars"?
A. Categorical nominal
B. Categorical ordinal
C. Quantitative discrete ✓
D. Quantitative continuous
Correct Answer: C
Rationale: Number of cars is a count (whole numbers), making it quantitative discrete. A — categorical
nominal has categories without order (e.g., car colors). B — categorical ordinal has ordered categories
(e.g., small/medium/large). D — continuous can take any value (e.g., weight, time). Tip: Discrete =
countable (whole numbers).
Q2: A dataset has a mean of 50 and a standard deviation of 5. According to the Empirical Rule,
approximately what percentage of data falls between 40 and 60?
A. 68%
B. 95% ✓
C. 99.7%
D. 50%
Correct Answer: B
Rationale: Mean=50, SD=5, so 40 is two standard deviations below (μ−2σ) and 60 is two above (μ+2σ).
Empirical Rule: 95% within ±2σ. A — 68% is within ±1σ (45-55). C — 99.7% within ±3σ (35-65). D —
incorrect. Tip: 68-95-99.7 rule = 1σ, 2σ, 3σ.
Q3: In a boxplot, which of the following represents the median?
A. Left edge of the box
B. Right edge of the box
C. Line inside the box ✓
D. Whisker endpoint
,Correct Answer: C
Rationale: The line inside the box is the median (Q2). A — left edge is Q1 (25th percentile). B — right
edge is Q3 (75th percentile). D — whisker endpoints are min and max (non-outlier). Tip: Boxplot = 5-
number summary: min, Q1, median, Q3, max.
Q4: A student's test scores are 85, 90, 78, 92, and 88. What is the median?
A. 85
B. 86.6
C. 88 ✓
D. 90
Correct Answer: C
Rationale: Sort: 78, 85, 88, 90, 92. Middle number = 88. A — 85 is Q1. B — 86.6 is the mean. D — 90 is
Q3. Tip: Median = middle value when sorted; average of two middle if even n.
Q5: A bag contains 3 red marbles, 2 blue marbles, and 5 green marbles. If one marble is drawn at
random, what is the probability it is not blue?
A. 0.2
B. 0.8 ✓
C. 0.5
D. 0.3
Correct Answer: B
Rationale: Total marbles = 10. Non-blue = 3 red + 5 green = 8. P(not blue) = 8/10 = 0.8. A — 0.2 is
P(blue). C — 0.5 = 5/10 (green only). D — 0.3 = 3/10 (red only). Tip: P(not A) = 1 − P(A) = 1 − 0.2 = 0.8.
Q6: The probability of event A is 0.4, event B is 0.5, and events A and B are mutually exclusive. What is
P(A or B)?
A. 0.1
B. 0.2
C. 0.7
D. 0.9 ✓
Correct Answer: D
Rationale: Mutually exclusive means P(A∩B)=0. P(A∪B)=P(A)+P(B)−P(A∩B)=0.4+0.5−0=0.9. A — 0.1 is
incorrect subtraction. B — 0.2 is P(A)×P(B) for independent, not mutually exclusive. C — 0.7 is
P(A)+P(B)−0.2 (wrong subtraction). Tip: Mutually exclusive = no overlap = simple addition.
,Q7: Which of the following is a requirement for a discrete probability distribution?
A. The sum of all probabilities equals 0
B. Each probability is greater than 1
C. The sum of all probabilities equals 1 and each probability is between 0 and 1 ✓
D. Each probability is negative
Correct Answer: C
Rationale: Valid probability distribution requires 0 ≤ P(x) ≤ 1 and ΣP(x)=1. A — sum must be 1, not 0. B —
probabilities cannot exceed 1. D — probabilities cannot be negative. Tip: Two rules: (1) between 0 and
1, (2) add to exactly 1.
Q8: A binomial experiment has n = 10 trials and probability of success p = 0.3. What is the mean
(expected value)?
A. 0.3
B. 3.0 ✓
C. 7.0
D. 10.0
Correct Answer: B
Rationale: Binomial mean μ = np = 10 × 0.3 = 3. A — 0.3 is p. C — 7 = n(1-p). D — 10 is n. Tip: Binomial
mean = n × p; variance = n × p × (1-p).
Q9: A z-score of −1.5 corresponds to which percentile approximately?
A. 7th percentile ✓
B. 16th percentile
C. 50th percentile
D. 93rd percentile
Correct Answer: A
Rationale: z = −1.5: area to the left is about 0.0668 ≈ 7th percentile. B — z = −1.0 is 16th percentile. C —
z = 0 is 50th percentile. D — z = +1.5 is 93rd percentile. Tip: Negative z = below mean = low percentile.
Q10: The heights of adult males are normally distributed with mean 70 inches and standard deviation
3 inches. What percentage of males are taller than 76 inches?
, A. 2.5% ✓
B. 5%
C. 16%
D. 95%
Correct Answer: A
Rationale: 76 inches = μ + 2σ (70+3+3). Empirical Rule: 95% within ±2σ, so 5% outside ±2σ. Half of that
(2.5%) is above +2σ. B — 5% is total outside ±2σ (both tails). C — 16% is above +1σ. D — 95% is within
±2σ. Tip: 68-95-99.7 rule works for quick estimates.
Q11: A random sample of 40 students has a mean GPA of 3.2 with a standard deviation of 0.5. What is
the standard error of the mean?
A. 0.0125
B. 0.0791 ✓
C. 0.5
D. 3.2
Correct Answer: B
Rationale: Standard error = σ/√n = 0.5/√40 = 0.5/6.3249 = 0.0791. A — 0.0125 = 0.5/40 (forgot sqrt). C
— 0.5 is sample SD, not SE. D — 3.2 is sample mean. Tip: SE = SD ÷ √n — divides by sqrt(n), not n.
Q12: According to the Central Limit Theorem, for which sample size does the sampling distribution of
the sample mean become approximately normal regardless of the population shape?
A. n ≥ 10
B. n ≥ 20
C. n ≥ 30 ✓
D. n ≥ 100
Correct Answer: C
Rationale: CLT states n ≥ 30 is sufficient for approximate normality of x. A, B — too small for non-normal
populations. D — also works but stricter than needed. Tip: n ≥ 30 = magic number for CLT.
Q13: A 95% confidence interval for a population mean is (45, 55). What is the margin of error?
A. 5 ✓
B. 10
C. 45
D. 50
Q1: A researcher collects data on the number of cars in a parking lot at 9 AM each day for 30 days.
What type of variable is "number of cars"?
A. Categorical nominal
B. Categorical ordinal
C. Quantitative discrete ✓
D. Quantitative continuous
Correct Answer: C
Rationale: Number of cars is a count (whole numbers), making it quantitative discrete. A — categorical
nominal has categories without order (e.g., car colors). B — categorical ordinal has ordered categories
(e.g., small/medium/large). D — continuous can take any value (e.g., weight, time). Tip: Discrete =
countable (whole numbers).
Q2: A dataset has a mean of 50 and a standard deviation of 5. According to the Empirical Rule,
approximately what percentage of data falls between 40 and 60?
A. 68%
B. 95% ✓
C. 99.7%
D. 50%
Correct Answer: B
Rationale: Mean=50, SD=5, so 40 is two standard deviations below (μ−2σ) and 60 is two above (μ+2σ).
Empirical Rule: 95% within ±2σ. A — 68% is within ±1σ (45-55). C — 99.7% within ±3σ (35-65). D —
incorrect. Tip: 68-95-99.7 rule = 1σ, 2σ, 3σ.
Q3: In a boxplot, which of the following represents the median?
A. Left edge of the box
B. Right edge of the box
C. Line inside the box ✓
D. Whisker endpoint
,Correct Answer: C
Rationale: The line inside the box is the median (Q2). A — left edge is Q1 (25th percentile). B — right
edge is Q3 (75th percentile). D — whisker endpoints are min and max (non-outlier). Tip: Boxplot = 5-
number summary: min, Q1, median, Q3, max.
Q4: A student's test scores are 85, 90, 78, 92, and 88. What is the median?
A. 85
B. 86.6
C. 88 ✓
D. 90
Correct Answer: C
Rationale: Sort: 78, 85, 88, 90, 92. Middle number = 88. A — 85 is Q1. B — 86.6 is the mean. D — 90 is
Q3. Tip: Median = middle value when sorted; average of two middle if even n.
Q5: A bag contains 3 red marbles, 2 blue marbles, and 5 green marbles. If one marble is drawn at
random, what is the probability it is not blue?
A. 0.2
B. 0.8 ✓
C. 0.5
D. 0.3
Correct Answer: B
Rationale: Total marbles = 10. Non-blue = 3 red + 5 green = 8. P(not blue) = 8/10 = 0.8. A — 0.2 is
P(blue). C — 0.5 = 5/10 (green only). D — 0.3 = 3/10 (red only). Tip: P(not A) = 1 − P(A) = 1 − 0.2 = 0.8.
Q6: The probability of event A is 0.4, event B is 0.5, and events A and B are mutually exclusive. What is
P(A or B)?
A. 0.1
B. 0.2
C. 0.7
D. 0.9 ✓
Correct Answer: D
Rationale: Mutually exclusive means P(A∩B)=0. P(A∪B)=P(A)+P(B)−P(A∩B)=0.4+0.5−0=0.9. A — 0.1 is
incorrect subtraction. B — 0.2 is P(A)×P(B) for independent, not mutually exclusive. C — 0.7 is
P(A)+P(B)−0.2 (wrong subtraction). Tip: Mutually exclusive = no overlap = simple addition.
,Q7: Which of the following is a requirement for a discrete probability distribution?
A. The sum of all probabilities equals 0
B. Each probability is greater than 1
C. The sum of all probabilities equals 1 and each probability is between 0 and 1 ✓
D. Each probability is negative
Correct Answer: C
Rationale: Valid probability distribution requires 0 ≤ P(x) ≤ 1 and ΣP(x)=1. A — sum must be 1, not 0. B —
probabilities cannot exceed 1. D — probabilities cannot be negative. Tip: Two rules: (1) between 0 and
1, (2) add to exactly 1.
Q8: A binomial experiment has n = 10 trials and probability of success p = 0.3. What is the mean
(expected value)?
A. 0.3
B. 3.0 ✓
C. 7.0
D. 10.0
Correct Answer: B
Rationale: Binomial mean μ = np = 10 × 0.3 = 3. A — 0.3 is p. C — 7 = n(1-p). D — 10 is n. Tip: Binomial
mean = n × p; variance = n × p × (1-p).
Q9: A z-score of −1.5 corresponds to which percentile approximately?
A. 7th percentile ✓
B. 16th percentile
C. 50th percentile
D. 93rd percentile
Correct Answer: A
Rationale: z = −1.5: area to the left is about 0.0668 ≈ 7th percentile. B — z = −1.0 is 16th percentile. C —
z = 0 is 50th percentile. D — z = +1.5 is 93rd percentile. Tip: Negative z = below mean = low percentile.
Q10: The heights of adult males are normally distributed with mean 70 inches and standard deviation
3 inches. What percentage of males are taller than 76 inches?
, A. 2.5% ✓
B. 5%
C. 16%
D. 95%
Correct Answer: A
Rationale: 76 inches = μ + 2σ (70+3+3). Empirical Rule: 95% within ±2σ, so 5% outside ±2σ. Half of that
(2.5%) is above +2σ. B — 5% is total outside ±2σ (both tails). C — 16% is above +1σ. D — 95% is within
±2σ. Tip: 68-95-99.7 rule works for quick estimates.
Q11: A random sample of 40 students has a mean GPA of 3.2 with a standard deviation of 0.5. What is
the standard error of the mean?
A. 0.0125
B. 0.0791 ✓
C. 0.5
D. 3.2
Correct Answer: B
Rationale: Standard error = σ/√n = 0.5/√40 = 0.5/6.3249 = 0.0791. A — 0.0125 = 0.5/40 (forgot sqrt). C
— 0.5 is sample SD, not SE. D — 3.2 is sample mean. Tip: SE = SD ÷ √n — divides by sqrt(n), not n.
Q12: According to the Central Limit Theorem, for which sample size does the sampling distribution of
the sample mean become approximately normal regardless of the population shape?
A. n ≥ 10
B. n ≥ 20
C. n ≥ 30 ✓
D. n ≥ 100
Correct Answer: C
Rationale: CLT states n ≥ 30 is sufficient for approximate normality of x. A, B — too small for non-normal
populations. D — also works but stricter than needed. Tip: n ≥ 30 = magic number for CLT.
Q13: A 95% confidence interval for a population mean is (45, 55). What is the margin of error?
A. 5 ✓
B. 10
C. 45
D. 50
