Statistics and Probability with Application

Choose an American household at random and let the random variable X be the number of cars (including SUVs and light trucks) they own. Here is the probability model if we ignore the few households that own more than 5 cars:

A housing company builds houses with two-car garages. What percent of households have more cars than the garage can hold?

• 13%

• 20%

• 45%

• 55%

• 80%

Choose an American household at random and let the random variable X be the number of cars (including SUVs and light trucks) they own. Here is the probability model if we ignore the few households that own more than 5 cars:

What’s the expected number of cars in a randomly selected American household?

• Between 0 and 5

• 1.00

• 1.75

• 1.84

• 2.00

A deck of cards contains 52 cards, of which 4 are aces. You are offered the following wager: Draw one card at random from the deck. You win $10 if the card drawn is an ace. Otherwise, you lose $1. If you make this wager very many times, what will be the mean amount you win?

• About −$1, because you will lose most of the time.

• About $9, because you win $10 but lose only $1.

• About −$0.15; that is, on average you lose about 15 cents.

• About $0.77; that is, on average you win about 77 cents.

• About $0, because the random draw gives you a fair bet.

The deck of 52 cards contains 13 hearts. Here is another wager: Draw one card at random from the deck. If the card drawn is a heart, you win $2. Otherwise, you lose $1. Compare this wager (call it Wager 2) with that of the previous exercise (call it Wager 1). Which one should you prefer?

• Wager 1, because it has a higher expected value.

• Wager 2, because it has a higher expected value.

• Wager 1, because it has a higher probability of winning.

• Wager 2, because it has a higher probability of winning.

• Both wagers are equally favorable.

The number of calories in a one-ounce serving of a certain breakfast cereal is a random variable with mean 110 and standard deviation 10. The number of calories in a cup of whole milk is a random variable with mean 140 and standard deviation 12. For breakfast, you eat one ounce of the cereal with 1/2 cup of whole milk. Let T be the random variable that represents the total number of calories in this breakfast. The MEAN of T is:

• 110

• 140

• 180

• 195

• 250

The number of calories in a one-ounce serving of a certain breakfast cereal is a random variable with mean 110 and standard deviation 10. The number of calories in a cup of whole milk is a random variable with mean 140 and standard deviation 12. For breakfast, you eat one ounce of the cereal with 1/2 cup of whole milk. Let T be the random variable that represents the total number of calories in this breakfast. The STANDARD DEVIATION of T is:

• 22

• 16

• 15.62

• 11.66

• 4

Joe reads that 1 out of 4 eggs contains salmonella bacteria. So he never uses more than 3 eggs in cooking. If eggs do or don’t contain salmonella independently of each other, the number of contaminated eggs when Joe uses 3 chosen at random has the following distribution:

• binomial; n = 4 and p = ¼

• binomial; n = 3 and p = 1/4

• binomial; n = 3 and p = 1/3

• geometric; p = ¼

• geometric; p = 1/3

Joe reads that 1 out of 4 eggs contains salmonella bacteria. So he never uses more than 3 eggs in cooking. The probability that at least 1 of Joe’s 3 eggs contains salmonella is about

• 0.84

• 0.68

• 0.58

• 0.42

• 0.30

Each entry in a table of random digits like Table D has probability 0.1 of being a 0, and digits are independent of each other. The mean number of 0s in a line 40 digits long is

• 10

• 4

• 3.098

• 0.4

• 0.1

Each entry in a table of random digits like Table D has probability 0.1 of being a 0, and digits are independent of each other. Ten lines in the table contain 400 digits. The count of 0s in these lines is approximately Normal with

• mean 40; standard deviation 36.

• mean 40; standard deviation 19.

• mean 40; standard deviation 6.

• mean 36; standard deviation 6.

• mean 10; standard deviation 19.