1. Random Variables Review Game

2. About 25% of those called for jury duty will find an excuse (work, poor health, travel, etc.) to avoid jury duty. If 12 people are called, what is the probability that less than 6 will not be available to serve?
Binomial
P(X < 6) = .9456

3. Choose a person aged 19 to 25 years at random and ask, “In the past seven days, how many times did you go to an exercise or fitness center or work out?” Based on a large sample survey, here is a probability model for the answer you will get:
What is the probability the person worked out at least once during the week?
Generic
P(X > 0) = .32

4. Choose a person aged 19 to 25 years at random and ask, “In the past seven days, how many times did you go to an exercise or fitness center or work out?” Based on a large sample survey, here is a probability model for the answer you will get:
What are the mean and standard deviation of the distribution?
Generic
μ = 1.03 days
Σ = 1.77 days

5. The EPA reports that 81% of Americans do not recycle garbage
The EPA reports that 81% of Americans do not recycle garbage. If 6 Americans are randomly selected, find the probability that at least two of them recycle.
P(X > 2) = .3201
Binomial

6. A study of 12,000 able-bodied male students at the University of Illinois found that their times for the mile run were approximately Normal with mean 7.11 minutes and standard deviation 0.74 minute. Choose a student at random from this group and call his time for the mile Y. Find P(Y < 6) and interpret the result.
P(X < 6) = .0668
Normal

7. One airline has found that 9% of the people who make reservations do not show. If the airline has accepted 220 reservations for a plane that has 210 seats, what is the probability that there are enough seats for all the passengers who show up?
Binomial
P(X < 210) = .9959

8. A survey of families in Statsylvania found that 12% of the households had no motor vehicles, 36% had one vehicle, 33% had two vehicles, 18% had three vehicles, and 1% had four vehicles. Find the mean and standard deviation for this distribution.
Generic
m = 1.6 & s = .95

9. An experiment consists of tossing a coin 10 times
An experiment consists of tossing a coin 10 times. What is the probability that the first head will occur on the fourth toss?
Geometric
P(X = 4) = .0625

10. According to the US Census Bureau, about 22% of American children under the age of 6 live in households with incomes below the official poverty level. A random sample of 400 children under the age of 6 is taken. What are the mean and standard deviation of children in the sample who come from households with incomes below the official poverty level?
Binomial
m = 88 & s = 8.28

11. Two independent random variables X and Y have the probability distributions, means, and standard deviations shown.
Let the random variable D = X − Y. Find the mean and standard deviation of D.
Combining
m = 0.1 & s = 1.8

12. Suppose a homeowner spends $300 for a home insurance policy that will pay out $200,000 if the home is destroyed by fire. Let Y = the profit made by the company on a single policy. From previous data, the probability that a home in this area will be destroyed by fire is What is the expected value of Y?
m = $260
Generic

13. The probability that a student is tardy to Statistics class is 0. 012
The probability that a student is tardy to Statistics class is (They just can’t wait to come to class!) How many students should Mrs. Goins expect to see before the first one is tardy?
Geometric
m = 83.33

14. Mr. Burgess and Mrs. Goins bowl every Tuesday night
Mr. Burgess and Mrs. Goins bowl every Tuesday night. Their scores follow an approximately normal distribution. Mr. Burgess has a mean of 212 and a standard deviation of 31. Mrs. Goins has a mean of 230 and a standard deviation of 40. Assuming their scores are independent, what is the probability that Mr. Burgess scores higher than Mrs. Goins on a randomly-selected Tuesday night?
Combining
P(X >0) = .361

15. Official records in a particular city show that the average number of days schools close in a school year due to flooding is 1.5 days. What is the probability that there will be 6 days schools are closed due to flooding in the next three years?
Poisson
P(X = 6) = .1281