Gaokao Exam Mathematics: Probability and Statistics 2 — Questions and Answers
Question 1: In a normal distribution, approximately what percentage of data falls within one standard deviation of the mean?
- 50%
- 68% (Correct answer)
- 95%
- 99.7%
Correct answer: 68%
The empirical (68-95-99.7) rule states that ~68% of data lies within ±1 standard deviation of the mean.
Question 2: A box contains 4 white and 6 black marbles. Two marbles are drawn without replacement. What is the probability both are white?
- 4/25
- 2/15 (Correct answer)
- 1/5
- 4/15
Correct answer: 2/15
P = (4/10) × (3/9) = 12/90 = 2/15.
Question 3: Which of the following correctly describes the variance of a dataset?
- The average of all data values
- The square root of the standard deviation
- The average of squared deviations from the mean (Correct answer)
- The difference between the maximum and minimum values
Correct answer: The average of squared deviations from the mean
Variance is defined as the average of the squared deviations of each data point from the mean.
Question 4: If a random variable X follows a binomial distribution with n = 10 and p = 0.5, what is E(X)?
- 2.5
- 5 (Correct answer)
- 7.5
- 10
Correct answer: 5
The expected value of a binomial distribution is E(X) = n × p = 10 × 0.5 = 5.
Question 5: A frequency table shows scores: 60 (5 students), 70 (8 students), 80 (7 students), 90 (5 students). What is the mode?
- 60
- 70 (Correct answer)
- 80
- 90
Correct answer: 70
The mode is 70 because it appears most frequently (8 students).
Question 6: Two independent events A and B have P(A) = 0.5 and P(B) = 0.6. What is P(A ∩ B)?
- 0.10
- 0.30 (Correct answer)
- 0.55
- 1.10
Correct answer: 0.30
For independent events, P(A ∩ B) = P(A) × P(B) = 0.5 × 0.6 = 0.30.
Gaokao Exam Mathematics: Probability and Statistics 2
In a normal distribution, approximately what percentage of data falls within one standard deviation of the mean?