Random Variable Examples

AP Statistics

Random Variable Examples

1. Suppose that each of three randomly selected customers purchasing a hot tub at a certain store chooses either an electric (E) or a gas (G) model. Assume that these customers make their choices independently of one another and that 40% of all customers select an electric model. The number among the three customers who purchase an electric hot tub is a random variable. What is the probability distribution?

2. Let X be the number of courses for which a randomly selected student at a certain university is registered. The probability distribution of random variable X appears in the accompanying table.

· What is ?

· What is the probability that the selected student is taking at most five courses?

· What is the probability that the selected student is taking more than five courses?

· What is ?

3. Below is a distribution for number of visits to a dentist in one year. X = # of visits to the dentist.

Determine the expected value, variance and standard deviation.

4. Let Y denote the number of broken eggs in a randomly selected carton of one dozen “store brand” eggs at a certain market. Suppose that the probability distribution of Y is as follows:

· Interpret =.20.

· Calculate the probability that the carton contains at most two broken eggs.

· Calculate the probability that the carton contains fewer than two broken eggs.

· Calculate the probability that the carton contains exactly ten unbroken eggs.

· Calculate the probability that the carton has at least ten eggs that are unbroken.

· Determine the expected number of broken eggs per dozen.

· Determine the variance and standard deviation.

5. Given we flip a coin 4 times. Let X = the number of heads. Determine the probability distribution and number of heads we would expect.

6. A club sells raffle tickets for $5 each. There are 10 prizes of $25 and one prize of $100. If 200 tickets are sold, determine the probability distribution. What are your expected winnings per ticket? Have you paid too much for the ticket (duh)? Explain.

7. Now that the new models are here, a car dealership has lowered prices on last year’s models. An aggressive salesperson estimates the following probability distribution of X, the number of cars that she’ll sell next week.

Determine the expected value, variance and standard deviation.

8. State whether each of the following random variables is discrete or continuous:

· The number of defective tires on a car.

· The body temperature of a hospital patient.

· The number of pages in a book.

· The number of draws (with replacement) from a deck of cards until a heart is selected.

· The lifetime of a light bulb.

9. Given the following density function represents a continuous random variable Z.

0 2

Describe the process to calculate the two probabilities. What can we say about their probabilities?

What is What is

10. The Lewis family has 3 kids. Every Sunday, Susan, the mom, buys either 1 or 2 gallons of milk. Below is the probability distribution for the number of gallons of milk bought at the store on Sunday.

Find the expected value and variance.

Over Christmas, grandparents come and visit. Susan will have to buy and extra gallon of milk. Complete the probability distribution for the number of gallons of milk bought.

Find the expected value and variance.

Next door to the Lewis family is the Onweagba family. They have 3 kids also. Unfortunately, the parents are sick, so Susan has agreed to do their shopping this Sunday. She will need to by double the amount of milk. Complete the probability distribution for the number of gallons of milk bought.

Find the expected value and variance.