Binomial Distribution 2

The random variable X ~ B(12, 0.2).

What is P(X = 3)?

Answer to 3 significant figures.

• 0.224

• 0.231

• 0.236

• 0.242

A random variable X has a distribution

X ~ B(10, p).

If var(X) = 1.875 what is the value of p, given that p < 0.5?

5% of the items produced by a machine are defective.

What is the probability that a batch of 12 contains at least 1 defective item? Answer to 4 decimal places.

Each of the 10 questions in a multiple choice test has 5 alternatives. Jim guesses the answer to each of the questions. What is the probability that Jim gets at most 4 questions correct? Answer to 3 decimal places.

In which of the following situations is X a binomial random variable.

Select all correct choices.

• X is the number of times a soccer captain calls the correct coin toss over a season of 38 matches in the UK Premier League.

• X is the number of times a student guesses in a multiple choice test of 40 questions until he guesses correctly.

• X is the number of defective items produced by a machine before and after maintenance

• X is number of boys in a 6-child family.

In a class of 12 children the probability that a child has blue eyes is 0.6. What is the probability of there being fewer than 8 blue-eyed children given that there more than 5 children have blue eyes?

Answer to 3 decimal places.

• 0.412

• 0.435

• 0.448

• 0.479

Which of the following are assumptions of a random variable X following a binomial distribution?

Select all correct responses.

• There must be a fixed number of trials

• All trials are independent of each other

• The probability of success must remain constant

• There can only be two outcomes, (which are usually called "success" or "failure")

A random variable X ~ B(10, 0.8). Which of the following probabilities has the SMALLEST value?

• P(X = 8)

• P(X > 8)

• P(5 < X < 8)

• P(X < 7)