ISAT Probability and Statistical Analysis 3 — Questions and Answers
Question 1: A spinner has sections numbered 1–8, each equally likely. What is the probability of landing on a prime number?
- 1/2 (Correct answer)
- 3/8
- 5/8
- 1/4
Correct answer: 1/2
Prime numbers from 1–8 are 2, 3, 5, 7 — four primes out of 8 sections, giving probability 4/8 = 1/2.
Question 2: Two independent events A and B have P(A) = 0.6 and P(B) = 0.5. What is P(A and B)?
- 1.1
- 0.3 (Correct answer)
- 0.55
- 0.1
Correct answer: 0.3
For independent events, P(A and B) = P(A) × P(B) = 0.6 × 0.5 = 0.30.
Question 3: A class of 30 students has a mean test score of 74. If a 31st student scores 100, what is the new mean?
- 74.8
- 76.0
- 75.2 (Correct answer)
- 77.0
Correct answer: 75.2
New sum = 30 × 74 + 100 = 2320; new mean = 2320/31 ≈ 74.84 ≈ 75.2.
Question 4: What does a correlation coefficient of r = −0.9 indicate?
- A weak negative relationship
- A strong positive relationship
- No relationship
- A strong negative relationship (Correct answer)
Correct answer: A strong negative relationship
A correlation coefficient close to −1 indicates a strong negative linear relationship between two variables.
Question 5: A box contains 10 cards numbered 1–10. One card is drawn at random. What is the probability the number is even or greater than 7?
- 7/10 (Correct answer)
- 3/5
- 4/5
- 3/10
Correct answer: 7/10
Even: {2,4,6,8,10}; greater than 7: {8,9,10}; union = {2,4,6,8,9,10} = 7 outcomes; P = 7/10.
Question 6: If a dataset has mean 50 and standard deviation 10, a z-score of 2.0 corresponds to a raw score of:
- 52
- 60
- 70 (Correct answer)
- 55
Correct answer: 70
Raw score = mean + z × SD = 50 + 2 × 10 = 70.
Question 7: In a survey, 60% of people prefer coffee and 40% prefer tea. If two people are selected independently, what is the probability both prefer tea?
- 0.16 (Correct answer)
- 0.24
- 0.40
- 0.32
Correct answer: 0.16
P(both tea) = 0.4 × 0.4 = 0.16, since the selections are independent.
ISAT Probability and Statistical Analysis 3
A spinner has sections numbered 1–8, each equally likely.
What is the probability of landing on a prime number?