AP Statistics Binomial and Geometric Probability

Which of the following is a true statement?

• The binomial setting requires that there are only two possible outcomes for each trial, while the geometric setting permits more than two outcomes.

• A geometric random variable takes on integer values from 0 to n.

• If X is a geometric random variable and the probability of success is 0.85, then the probability distribution of X will be skewed left, since 0.85 is closer to 1 than to 0.

• There is a fixed number of trials in a geometric setting, and the number of trials varies in a binomial setting.

• The distribution of every geometric random variable is skewed right

A spinner has 5 equally-sized regions (blue, green, red, orange, and yellow). If you spin the spinner 20 times, what is the probability that the spinner lands on blue at most 5 times?

• Approximately 0

• 0.370

• 0.630

• 0.804

• Approximately 1

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. 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 standard deviation of X is 1.27. Interpret this value.

• The number of computers in a randomly selected household is within 1.27 of the mean.

• The number of computers in a randomly selected household is exactly 1.27 from the mean.

• The number of computers in a randomly selected household is 1.27, on average.

• The number of computers in a randomly selected household is typically 1.27 from the mean.

• The average number of computers in a randomly selected household is typically 1.27 from the mean.

• A

• B

• C

• D

• F

• A

• B

• C

• D

• E

A teacher gives a 10-question multiple-choice quiz. Each question has four possible answers, and a student randomly guesses the answers to all 10 questions. What is the probability that the student gets at least 8 questions correct?

• A. 0.0034

• B. 0.0193

• C. 0.0439

• D. 0.1094

Is this binomial experiment? Shuffle a deck of 52 cards. Turn over the top card. Do not replace the card. Repeat the process 5 times. Let X = the card you observe.

• Yes

• No, the trials are not identical.

When rolling a fair die 100 times, what is the probability of rolling a "4" exactly 25 times?

• 1.0%

• 16.7%

• 25%

• 2.1%

The American College of Obstetricians and Gynecologists reports that 32% of all births in the United States take place by Caesarian section each year. Five woman are about to give birth.

What is the binomial probability that less than 3 will have a C-section birth?

• 0.0391

• 0.1906

• 0.9609

• 0.8095

Answer explanation

Binomial Probability Formula!

n = 5

p = 0.32

q = 1 - p = 0.68

x is "less than 3", so you have to find the probability when x is 2, 1 and 0. Then add them together.

p(0) = 0.1454

p(1) = 0.3421

p(2)=0.322

So, 0.1454 + 0.3421 + 0.322 = 0.8095