WorksheetsChapter 6 AP Stat Free Response
Total questions: 28
Worksheet time: 2hrs 20mins
Let the random variable X represent the profit made on a randomly selected day by a certain store. Assume that X is approximately Normal with mean $360 and standard deviation $50. The least profitable 10% of days have a profit of at most how many dollars?
$244
$296
$370
$424
$476
Which of the following random variables is discrete?
The number of shots made in 10 free-throw attempts.
The weight of a rhinoceros.
The species of an insect.
The length of a needle on a saguaro cactus.
None of the variables above are discrete.
A marketing survey compiled data on the number of personal computers in households. If X = the number of computers in a randomly-selected household, and we omit the rare cases of more than 5 computers, then X has the given distribution. The expected value of X is E(X) =
0.40
1.00
1.45
1.66
2.50
A marketing survey compiled data on the number of personal computers in households. X = the number of computers in a randomly-selected household. If you were to randomly select households, what is the probability it would take exactly 8 selections to find one with 5 computers?
Approximately 0
0.02
0.03
0.32
Approximately 1
The number of DVDs rented daily at DVD rental machine has a mean of 134 with a standard deviation of 32.
Select two days at random and find the difference in the number of DVDs rented on the two days. What are the mean and standard deviation of the difference in the number of DVDs rented?
Mean = 0, Standard Deviation = 0
Mean = 0, Standard Deviation = 64
Mean = 0, Standard Deviation = 45
Mean = 92, Standard Deviation = 32
Mean = 134, Standard Deviation = 32
The number of DVDs rented daily at DVD rental machine has a mean of 134 with a standard deviation of 32.
The cost of the electricity to keep the DVD rental machine on is $1.45 per day. Each DVD rental increases the electricity cost by $0.02. What are the mean and standard deviation of the electricity cost per day?
Mean = $4.13, Standard Deviation = $0.64
Mean = $4.13, Standard Deviation = $1.77
Mean = $4.13, Standard Deviation = $2.09
Mean = $2.68, Standard Deviation = $0.64
Mean = $2.68, Standard Deviation = $2.09
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
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 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 standard deviation of T is...
22
16
15.62
11.66
It turns out that 25 seniors at Fashionable High School took both the AP Statistics exam and the AP Spanish Language exam. The mean score on the Statistics exam for the 25 seniors was 2.4 with standard deviation of 0.6, and the mean score on the Spanish Language exam was 2.65 with a standard deviation of 0.55. We want to combine the scores into a single score. What are the correct mean and standard deviation of the combined scores?
5.05; 1.15
5.05; 1.07
5.05; 0.66
5.05; 0.81
5.05; You cannot determine the standard deviation from this information.
The following table gives the probabilities of various outcomes for a gambling game. What is the player's expected return on a bet of $1?
$0.05
-$0.60
-$0.05
-$0.10
You can't answer this question since this is not a complete probability distribution.
Let the random variable X represent the amount of money George makes when delivering pizzas in a randomly selected week during the year. Assume that X is Normal with a mean of $362 and a standard deviation of $70. The probability is approximately 0.75 that, in a randomly elected week, George will make less than...
$416.14
$314.78
$409.21
$362
$377.86
A test for extrasensory perception (ESP) involves asking a person to tell which of 5 shapes - a circle, star, triangle, diamond, or heart - appears on a hidden computer screen. On each trial, the computer is equally likely to select any of the 5 shapes. Suppose researchers are testing a person who does not have ESP and so is just guessing on each trial. What is the probability that the person guesses the first 4 shapes incorrectly but gets the 5th correct?
(4/5)4
(4/5)4 * (1/5)
(5/1) * (4/5)4 * (1/5)
A fast-food restaurant runs a promotion in which certain food items come with game pieces. According to the restaurant, 1 in 4 game pieces is a winner. If Jeff gets 4 game pieces, what is the probability that he wins exactly 1 price?
Joe reads that 1 our 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 = 1/4
Binomial; n = 3 and p = 1/4
Binomial; n = 3 and p = 1/3
Geometric; p = 1/4
Geometric; p = 1/3
For which of the following counts would a binomial probability model be reasonable?
The number of traffic tickets written by each police officer in a large city during one month.
The number of hearts in a hand of five cards dealt from a standard deck of 52 cards that has been thoroughly shuffled.
The number of 7’s in a randomly selected set of five random digits from a table of random digits.
The number of phone calls received in a one-hour period.
All of the above.
Assuming the probability of having a child of either gender is 50%, what is the probability that a family doesn't have a baby girl until their third child?
0.13
0.15
0.05
0.88
The probability that Jalen makes a free throw is 75% (assume each attempt is independent). Which of the following would correctly calculate the probability of getting the first successful free throw on the 5th attempt?
geometcdf with p=5 and x = 0.75
geometpdf with p=0.75 and x = 5
geometpdf with p = 5 and x = 0.75
geometcdf with p = 0.75 and x = 5
The standard deviation of X is ox = 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 by 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.
