FAST Probability and Distributions 3

Question 1

In a binomial experiment with n=10 and p=0.3, what is the expected number of successes?

Accepted Answer

3

Answer

The expected value of a binomial distribution is E(X) = n × p = 10 × 0.3 = 3.

Question 2

What does a z-score of 2.0 indicate about a data point?

Accepted Answer

It is 2 standard deviations above the mean

Answer

A z-score of 2.0 means the data point is exactly 2 standard deviations above the mean.

Question 3

Events A and B are independent. P(A) = 0.6 and P(B) = 0.5. What is P(A and B)?

Accepted Answer

0.3

Answer

For independent events, P(A and B) = P(A) × P(B) = 0.6 × 0.5 = 0.3.

Question 4

A dataset follows a uniform distribution between 10 and 30. What is the probability that a randomly selected value falls between 15 and 25?

Accepted Answer

1/2

Answer

For a uniform distribution, P(15 ≤ X ≤ 25) = (25−15)/(30−10) = 10/20 = 1/2.

Question 5

A test has 5 multiple-choice questions each with 4 options. If a student guesses randomly, what is the probability of getting all 5 correct?

Accepted Answer

1/1024

Answer

Each question has a 1/4 chance of being correct, so all 5 correct = (1/4)^5 = 1/1024.

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