Chapter 5, AP Statistics

Which of the following random variables is geometric?

• The number of times I have to roll a die to get two 6s.

• The number of cards I deal from a well-shuffled deck of 52 cards until I get a heart.

• The number of digits I read in a randomly selected row of the random digits table until I find a 7.

• The number of 7s in a row of 40 random digits.

• The number of 6s I get if I roll a die 10 times.

Seventeen people have been exposed to a particular disease. Each one independently has a 40% chance of contracting the disease. A hospital has the capacity to handle 10 cases of the disease. What is the probability that the hospital’s capacity will be exceeded?

• 0.011

• 0.965

• 0.035

• 0.989

• 0.092

In which of the following situations would it be appropriate to use a Normal distribution to approximate probabilities for a binomial distribution with the given values of n and p?

• n = 10, p = 0.5

• n = 40, p = 0.88

• n = 100, p = 0.2

• n = 100, p = 0.99

• n = 1000, p = 0.003

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.

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

• 0.93

• 0.20

• 0.13

• 0.07

The probability that an American household will have at least 2 cars is...

• 0.55

• 0.35

• 0.45

• 0.93

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

• 1.00

• 1.75

• 1.84

• 2.00

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.