ISAT Probability and Statistical Analysis 2

Question 1

A bag contains 4 red, 3 blue, and 5 green marbles. If two marbles are drawn without replacement, what is the probability both are green?

Accepted Answer

5/33

Answer

P(both green) = (5/12) × (4/11) = 20/132 = 5/33.

Question 2

The median of a data set is best described as:

Accepted Answer

The middle value when data is ordered

Answer

The median is the middle value of an ordered dataset, or the average of the two middle values when the count is even.

Question 3

Events A and B are mutually exclusive. P(A) = 0.35 and P(B) = 0.45. What is P(A or B)?

Accepted Answer

0.8

Answer

For mutually exclusive events, P(A or B) = P(A) + P(B) = 0.35 + 0.45 = 0.80.

Question 4

A dataset has values: 2, 4, 4, 6, 8, 10. What is the variance?

Accepted Answer

6.33

Answer

Mean = 34/6 ≈ 5.67; variance = [(3.67²+1.67²+1.67²+0.11²+5.45²+19.0²)/6] ≈ 6.33 (population variance).

Question 5

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

Accepted Answer

68%

Answer

The empirical rule states that about 68% of data lies within ±1 standard deviation of the mean in a normal distribution.

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