CHAMBERLAIN COLLEGE OF NURSING
MATH 225N WEEK 5: PROBABILITY
AND NORMAL DISTRIBUTIONS
QUESTIONS AND VERIFIED ANSWERS
|100% CORRECT| GRADE A+
1. A nurse is reviewing the distribution of birth weights in a neonatal unit, which follows a
normal distribution with a mean of 3.5 kg and a standard deviation of 0.5 kg. What is the z-
score for a baby weighing 4.2 kg?
A. 1.2
B. 0.7
C. -1.4
D. 1.4
Answer: D
Conceptual Explanation: The z-score is calculated as (x - mean) / standard deviation. (4.2
- 3.5) / 0.5 = 0..5 = 1.4.
2. Which of the following properties is NOT a characteristic of the standard normal
distribution?
A. The total area under the curve is equal to 1.0.
,B. The distribution is skewed to the right depending on the sample size.
C. The mean is equal to 0.
D. The standard deviation is equal to 1.
Answer: B
Conceptual Explanation: The standard normal distribution is always symmetric and bell-
shaped, not skewed. Its mean is 0 and standard deviation is 1.
3. In a binomial distribution where n = 20 and p = 0.4, what is the calculated mean (expected
value)?
A. 12
B. 4
C. 4.8
D. 8
Answer: D
Conceptual Explanation: For a binomial distribution, the mean is n * p. 20 * 0.4 = 8.
4. According to the Central Limit Theorem, as the sample size (n) increases, the distribution of
the sample mean approaches:
A. The Poisson distribution
B. The original population distribution
, C. A normal distribution
D. A uniform distribution
Answer: C
Conceptual Explanation: The Central Limit Theorem states that as sample size increases
(typically n >= 30), the sampling distribution of the mean will be approximately normal
regardless of the population’s shape.
5. If a patient’s systolic blood pressure follows a normal distribution with a mean of 120 and a
standard deviation of 10, what is the probability that a randomly selected patient has a
pressure between 110 and 130?
A. 0.95
B. 0.68
C. 0.997
D. 0.50
Answer: B
Conceptual Explanation: Based on the Empirical Rule (68-95-99.7), approximately 68%
of the data falls within one standard deviation (120 - 10 to 120 + 10) of the mean.
6. A study finds that 15% of patients experience a side effect. If 10 patients are treated, what
is the probability that exactly 2 experience the side effect? (Use binomial formula)
A. 0.2298
MATH 225N WEEK 5: PROBABILITY
AND NORMAL DISTRIBUTIONS
QUESTIONS AND VERIFIED ANSWERS
|100% CORRECT| GRADE A+
1. A nurse is reviewing the distribution of birth weights in a neonatal unit, which follows a
normal distribution with a mean of 3.5 kg and a standard deviation of 0.5 kg. What is the z-
score for a baby weighing 4.2 kg?
A. 1.2
B. 0.7
C. -1.4
D. 1.4
Answer: D
Conceptual Explanation: The z-score is calculated as (x - mean) / standard deviation. (4.2
- 3.5) / 0.5 = 0..5 = 1.4.
2. Which of the following properties is NOT a characteristic of the standard normal
distribution?
A. The total area under the curve is equal to 1.0.
,B. The distribution is skewed to the right depending on the sample size.
C. The mean is equal to 0.
D. The standard deviation is equal to 1.
Answer: B
Conceptual Explanation: The standard normal distribution is always symmetric and bell-
shaped, not skewed. Its mean is 0 and standard deviation is 1.
3. In a binomial distribution where n = 20 and p = 0.4, what is the calculated mean (expected
value)?
A. 12
B. 4
C. 4.8
D. 8
Answer: D
Conceptual Explanation: For a binomial distribution, the mean is n * p. 20 * 0.4 = 8.
4. According to the Central Limit Theorem, as the sample size (n) increases, the distribution of
the sample mean approaches:
A. The Poisson distribution
B. The original population distribution
, C. A normal distribution
D. A uniform distribution
Answer: C
Conceptual Explanation: The Central Limit Theorem states that as sample size increases
(typically n >= 30), the sampling distribution of the mean will be approximately normal
regardless of the population’s shape.
5. If a patient’s systolic blood pressure follows a normal distribution with a mean of 120 and a
standard deviation of 10, what is the probability that a randomly selected patient has a
pressure between 110 and 130?
A. 0.95
B. 0.68
C. 0.997
D. 0.50
Answer: B
Conceptual Explanation: Based on the Empirical Rule (68-95-99.7), approximately 68%
of the data falls within one standard deviation (120 - 10 to 120 + 10) of the mean.
6. A study finds that 15% of patients experience a side effect. If 10 patients are treated, what
is the probability that exactly 2 experience the side effect? (Use binomial formula)
A. 0.2298
