MATH 225N Statistics Final Exam
2026/2027 |Statistics Final Examination
with Complete Questions & Verified
Answers | Latest Version
1. A dataset has mean 50 and standard deviation 5. What is the z-score for
a value of 60?
✅
A. 1.0
B. 2.0
C. 0.5
D. 1.5
Solution:
( z = \frac{x - \mu}{\sigma} = \frac{60 - 50}{5} = \frac{10}{5} = 2.0 )
2. If a probability distribution has P(A) = 0.3 and P(B) = 0.5, and A and B are
mutually exclusive, what is P(A ∪ B)?
A. 0.8✅
B. 0.15
C. 0.2
D. 0.5
Solution:
For mutually exclusive events: ( P(A ∪ B) = P(A) + P(B) = 0.3 + 0.5 = 0.8 )
3. The variance of a dataset is 25. What is the standard deviation?
A. 5 ✅
B. 25
,C. 10
D. 15
Solution:
Standard deviation ( \sigma = \sqrt{variance} = \sqrt{25} = 5 )
4. A die is rolled. What is the probability of getting an even number?
✅
A. 1/6
B. 1/2
C. 1/3
D. 2/3
Solution:
Even numbers: 2, 4, 6 → 3 outcomes / 6 total outcomes → ( P = 3/6 = 1/2 )
5. A sample of 25 students has mean 70. The population standard deviation
is 10. What is the standard error of the mean (SEM)?
A. 2 ✅
B. 10
C. 0.4
D. 5
Solution:
( SEM = \frac{\sigma}{\sqrt{n}} = \frac{10}{\sqrt{25}} = \frac{10}{5} = 2 )
6. A 95% confidence interval for a population mean is calculated as 50 ± 4.
What is the margin of error?
✅
A. 50
B. 4
C. 54
D. 46
Solution:
The margin of error is the amount added/subtracted from the sample mean → 4
, 7. Which of the following is a continuous random variable?
✅
A. Number of students in a class
B. Height of students
C. Number of cars in a parking lot
D. Number of phone calls per day
Solution:
Continuous variables can take any value within a range → height can be 160.2 cm, 160.25
cm, etc.
8. A dataset: 5, 7, 7, 8, 10. What is the mode?
✅
A. 5
B. 7
C. 8
D. 10
Solution:
Mode = most frequently occurring value → 7 appears twice, others once.
9. If P(A) = 0.6 and P(B) = 0.4 and A and B are independent, what is P(A ∩
B)?
A. 0.24 ✅
B. 0.1
C. 1.0
D. 0.6
Solution:
For independent events: ( P(A ∩ B) = P(A) × P(B) = 0.6 × 0.4 = 0.24 )
10. In a normal distribution, approximately what percent of values lie within
1 standard deviation of the mean?
✅
A. 50%
B. 68%
C. 95%
D. 99%
2026/2027 |Statistics Final Examination
with Complete Questions & Verified
Answers | Latest Version
1. A dataset has mean 50 and standard deviation 5. What is the z-score for
a value of 60?
✅
A. 1.0
B. 2.0
C. 0.5
D. 1.5
Solution:
( z = \frac{x - \mu}{\sigma} = \frac{60 - 50}{5} = \frac{10}{5} = 2.0 )
2. If a probability distribution has P(A) = 0.3 and P(B) = 0.5, and A and B are
mutually exclusive, what is P(A ∪ B)?
A. 0.8✅
B. 0.15
C. 0.2
D. 0.5
Solution:
For mutually exclusive events: ( P(A ∪ B) = P(A) + P(B) = 0.3 + 0.5 = 0.8 )
3. The variance of a dataset is 25. What is the standard deviation?
A. 5 ✅
B. 25
,C. 10
D. 15
Solution:
Standard deviation ( \sigma = \sqrt{variance} = \sqrt{25} = 5 )
4. A die is rolled. What is the probability of getting an even number?
✅
A. 1/6
B. 1/2
C. 1/3
D. 2/3
Solution:
Even numbers: 2, 4, 6 → 3 outcomes / 6 total outcomes → ( P = 3/6 = 1/2 )
5. A sample of 25 students has mean 70. The population standard deviation
is 10. What is the standard error of the mean (SEM)?
A. 2 ✅
B. 10
C. 0.4
D. 5
Solution:
( SEM = \frac{\sigma}{\sqrt{n}} = \frac{10}{\sqrt{25}} = \frac{10}{5} = 2 )
6. A 95% confidence interval for a population mean is calculated as 50 ± 4.
What is the margin of error?
✅
A. 50
B. 4
C. 54
D. 46
Solution:
The margin of error is the amount added/subtracted from the sample mean → 4
, 7. Which of the following is a continuous random variable?
✅
A. Number of students in a class
B. Height of students
C. Number of cars in a parking lot
D. Number of phone calls per day
Solution:
Continuous variables can take any value within a range → height can be 160.2 cm, 160.25
cm, etc.
8. A dataset: 5, 7, 7, 8, 10. What is the mode?
✅
A. 5
B. 7
C. 8
D. 10
Solution:
Mode = most frequently occurring value → 7 appears twice, others once.
9. If P(A) = 0.6 and P(B) = 0.4 and A and B are independent, what is P(A ∩
B)?
A. 0.24 ✅
B. 0.1
C. 1.0
D. 0.6
Solution:
For independent events: ( P(A ∩ B) = P(A) × P(B) = 0.6 × 0.4 = 0.24 )
10. In a normal distribution, approximately what percent of values lie within
1 standard deviation of the mean?
✅
A. 50%
B. 68%
C. 95%
D. 99%
