Discrete Probability Distributions

Problem 4

Determine whether the random variable is discrete or continuous.

1. The number of marbles in a bag.
2. The distance a baseball travels in the air after being hit.
3. The square footage of a house.
4. The weight of an airplane.
5. The number of points scored in a basketball game.

According to a survey by paint manufacturer, DuPont, 22% of all cars in the United States are red. Suppose 20 cars are randomly selected and the number of red cars are recorded. Round probabilities to 4 decimal places.

1. Explain why this is a binomial experiment.

1. Find and interpret the probability that exactly 6 cars are red.

1. Find and interpret the probability that fewer than 6 cars are red.

1. Find and interpret the probability that at least 6 cars are red.

1. Compute the mean and standard deviation of the binomial random variable.