AP Statistics Chapter 4 Review

The weight of tomatoes chosen at random from a bin at the farmer’s market follows a Normal distribution with mean = 10 ounces and standard deviation  = 1 ounce. Suppose we pick four tomatoes at random from the bin and find their total weight T. The random variable T is

• Normal, with mean 10 ounces and standard deviation 1 ounce.

• Normal, with mean 40 ounces and standard deviation 2 ounces

• Normal, with mean 40 ounces and standard deviation 4 ounces

• binomial, with mean 40 ounces and standard deviation 2 ounces

• binomial, with mean 40 ounces and standard deviation 4 ounces.

The probability that an American household will have at most 3 cars is...

• 0.93

• 0.20

• 0.13

• 0.07

The standard deviation of X is o_x = 1.08. If many households were selected at random, which of the following would be the best interpretation of the value 1.08?

• The mean number of cars would be about 1.08.

• If we randomly selected many households, the number of cars would typically vary be about 1.08 cars from the mean.

• The number of cars would be at most 1.08 from the mean.

• The number of cars would be within 1.08 from the mean about 68% of the time.

• The mean number of cars would be about 1.08 from the expected value.

A certain vending machine offers 20-ounce bottles of soda for $1.50. The number of bottles X bought from the machine on any day is a random variable with mean 50 and standard deviation 15. Let the random variable Y equal the total revenue from this machine on a given day. Assume the machine works properly and that no sodas are stolen from the machine. What are the mean and standard deviation of Y?

• Mean Y = $1.50 and St. Dev Y = $22.50

• Mean Y = $1.50 and St. Dev Y = $33.75

• Mean Y = $75 and St. Dev Y = $18.37

• Mean Y = $75 and St. Dev Y = $22.50

• Mean Y = $75 and St. Dev Y = $33.75

A binomial event has n = 60 trials. The probability of success on each trial is 0.4. Let X be the count of successes of the event during the 60 trials. What are mean X and standard deviation X?

• 24; 3.79

• 24; 14.4

• 4.9; 3.79

• 4.9; 14.4

The GPA of students who take the AP Statistics exam are approximately normally distributed with a mean of 3.4 with a standard deviation of 0.3. What is the probability that a student selected at random from this group has a GPA lower than 3?

• 0.0918

• 0.4082

• 0.9082

• -0.0918

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

• 1.00

• 1.75

• 1.84

• 2.00

How would you interpret the expected value in number 3?

• The maximum number of cars for the household is Exp(C).

• The average number of cars for the household is Exp(C).

• If we randomly select many households, the average number of cars per household will be approximately by Exp(C).

• If we randomly select many households, the average number of cars per household will vary approximately by Exp(C).

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 number of calories in a 1-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 1 ounce of the cereal and 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