Gaokao Exam Mathematics: Probability and Statistics 2

Question 1

In a normal distribution, approximately what percentage of data falls within one standard deviation of the mean?

Accepted Answer

68%

Answer

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?

Accepted Answer

2/15

Answer

P = (4/10) × (3/9) = 12/90 = 2/15.

Question 3

Which of the following correctly describes the variance of a dataset?

Accepted Answer

The average of squared deviations from the mean

Answer

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)?

Accepted Answer

5

Answer

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?

Accepted Answer

70

Answer

The mode is 70 because it appears most frequently (8 students).

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