Probability

Q. How many ways can you choose 3 items from a set of 10?

Solution

C(10,3) = 10! / (3!(10-3)!) = 120.

Correct Answer: B — 210

Q. If you flip a fair coin three times, what is the probability of getting exactly two heads?

Solution

The probability of getting exactly 2 heads in 3 flips = C(3,2) * (1/2)^2 * (1/2)^1 = 3/8.

Correct Answer: B — 3/8

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

Solution

In a normal distribution, approximately 68% of the data falls within one standard deviation of the mean.

Correct Answer: B — 68%

Q. What is the mean of the following data set: 4, 8, 6, 5, 3?

Solution

Mean = (4 + 8 + 6 + 5 + 3) / 5 = 26 / 5 = 5.2

Correct Answer: C — 6

Q. What is the median of the following data set: 7, 3, 5, 9, 1?

Solution

First, sort the data: 1, 3, 5, 7, 9. The median is the middle value, which is 5.

Correct Answer: B — 5

Q. What is the mode of the following data set: 2, 3, 4, 4, 5, 5, 5?

Solution

The mode is the number that appears most frequently, which is 5.

Correct Answer: D — 5

Q. What is the probability of rolling a sum of 7 with two six-sided dice?

Solution

There are 6 combinations to get a sum of 7 out of 36 total combinations, so the probability is 6/36 = 1/6.

Correct Answer: D — 5/36

Q. What is the standard deviation of the data set: 10, 12, 23, 23, 16, 23, 21?

Solution

Standard deviation = sqrt(variance) = sqrt(8.57) ≈ 2.93.

Correct Answer: A — 4.5

Q. What is the variance of the data set: 1, 2, 3, 4, 5?

Solution

Variance = [(1-3)^2 + (2-3)^2 + (3-3)^2 + (4-3)^2 + (5-3)^2] / 5 = 2

Correct Answer: B — 2.5

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