Discrete Probability Distributions

Determine whether the random variable is discrete or continuous.

1. The number of light bulbs in a room.
2. The time it takes to fly from Chicago to Los Angeles.
3. The number of hits to a website in a day.
4. The amount of show in Denver during the winter.
5. The number of patients in the emergency room on a given day.

According to the American Lung Association, 90% of adult smokers started smoking before turning 21 years old. Ten smokers 21 years old or older are randomly selected and the number of smokers who started smoking before age 21 is recorded. Round probabilities to 4 decimal places.

1. Explain why this is a binomial experiment.

1. Find and interpret the probability that exactly 8 of them started smoking before age 21.

1. Find and interpret the probability that fewer than 8 of them started smoking before age 21.

1. Find and interpret the probability that at least 8 of them started smoking before age 21.

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

Discrete Probability Distributions

Determine whether the random variable is discrete or continuous.

1. The weight of a T-bone steak.
2. The time it takes for a light bulb to burn out.
3. The number of free throw attempts in a basketball game.
4. The number of people with blood.
5. The height of a basketball player.

According to flightstats.com, American Airlines flights from Dallas to Chicago are on time 80% of the time. Suppose 15 flights are randomly selected and the number of on-time flights is recorded. Round probabilities to 4 decimal places.

1. Explain why this is a binomial experiment.

1. Find and interpret the probability that exactly 10 flights are on time.

1. Find and interpret the probability that fewer than 10 flights are on time.

1. Find and interpret the probability that at least 10 flights are on time.

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

Discrete Probability Distributions

Problem 3

Determine whether the random variable is discrete or continuous.

1. The amount of rain in Seattle during the April.
2. The number of customers arriving at a bank between noon and 1:00 pm.
3. The number of athletes participating in the 2016 Summer Olympics.
4. The time required to download a file from the internet.
5. The distance traveled from your work to your home.

According to the High School Athletics Participation Survey, 55% of students enrolled in high school participate in athletic programs. Suppose 12 high school students are randomly selected and the number who participate in athletic programs is recorded. Round probabilities to 4 decimal places.

1. Explain why this is a binomial experiment.

1. Find and interpret the probability that exactly 7 high school students participate in athletic programs.

1. Find and interpret the probability that fewer than 7 high school students participate in athletic programs.

1. Find and interpret the probability that at least 7 high school students participate in athletic programs.

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

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.

Discrete Probability Distributions

Problem 5

Determine whether the random variable is discrete or continuous.

1. The distance traveled from your home to your school.
2. The number of students in your Statistics class.
3. The number of patients in the doctor's office on a given day.
4. The time it takes to fly from Chicago to Detroit.
5. The number of books in the public library.

According to the American Community Survey, 27% of residents of the United States 25 years old or older had earned a bachelor degree. Suppose you select 12 residents of the United States 25 years old or older and recorded the number who had earned a bachelor degree. Round probabilities to 4 decimal places.

1. Explain why this is a binomial experiment.

1. Find and interpret the probability that exactly 5 of them had a bachelor degree.

1. Find and interpret the probability that fewer than 5 of them had a bachelor degree.

1. Find and interpret the probability that at least 5 of them had a bachelor degree.

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