NSAA NSAA Mathematics - Statistics and Probability 2 — Questions and Answers
Question 1: In a normal distribution, approximately what percentage of data lies within one standard deviation of the mean?
- 50%
- 68% (Correct answer)
- 95%
- 99.7%
Correct answer: 68%
The 68-95-99.7 rule states that ~68% of data falls within ±1 standard deviation of the mean.
Question 2: How many ways can 4 books be arranged on a shelf?
- 4
- 12
- 16
- 24 (Correct answer)
Correct answer: 24
The number of arrangements = 4! = 4×3×2×1 = 24.
Question 3: A card is drawn from a standard 52-card deck. What is the probability that it is a heart or a king?
- 4/13
- 17/52 (Correct answer)
- 16/52
- 1/4
Correct answer: 17/52
P(heart) = 13/52, P(king) = 4/52, P(king of hearts) = 1/52; P(heart or king) = 13/52 + 4/52 - 1/52 = 16/52 = 4/13.
Question 4: The interquartile range (IQR) is calculated as:
- Q1 - Q3
- Q3 - Q1 (Correct answer)
- Q3 - median
- median - Q1
Correct answer: Q3 - Q1
IQR = Q3 - Q1, the difference between the upper and lower quartiles.
Question 5: From a group of 5 people, how many ways can a committee of 3 be chosen?
- 6
- 10 (Correct answer)
- 15
- 20
Correct answer: 10
C(5,3) = 5!/(3!2!) = 10.
Question 6: What is P(A|B) if P(A∩B) = 0.12 and P(B) = 0.4?
- 0.048
- 0.3 (Correct answer)
- 0.52
- 3.33
Correct answer: 0.3
P(A|B) = P(A∩B)/P(B) = 0.12/0.4 = 0.3.
NSAA NSAA Mathematics - Statistics and Probability 2
In a normal distribution, approximately what percentage of data lies within one standard deviation of the mean?