AP Stats Probability Distributions

There are 20 multiple-choice questions on an exam, each having four possible responses, of which only one is correct. Each question is worth 5 points if answered correctly. Suppose that a student guesses the answer to each question, with her guesses from question to question being independent. The student's expected (mean) score on this exam is

• 5

• 15

• 25

• 50

There are 20 multiple-choice questions on an exam, each having four possible responses, of which only one is correct. Each question is worth 5 points if answered correctly. Suppose that a student guesses the answer to each question, with her guesses from question to question being independent. The standard deviation of the student's score on the exam is

• 1.94

• 4.33

• 9.68

• 21.65

In a certain large population, 70% are right-handed. You need a left-handed pitcher for your softball team and decide to find one by asking people chosen from the population at random. (We assume that once you do find a left-hander, he or she will be happy to join your team and will say yes.) Which of the following expression gives the probability that the first left-hander you finder is the fourth person you ask?

In a certain large population, 70% are right-handed. You need a left-handed pitcher for your softball team and decide to find one by asking people chosen from the population at random. (We assume that once you do find a left-hander, he or she will be happy to join your team and will say yes.) Which of the following is closest to the probability that you will have to ask four or more people before finding your first left-hander?

• 0.103

• 0.657

• 0.343

• 0.027

A random sample of 83 residents of a certain town were asked whether they approve of a proposal to improve the town’s aging bridges. The 95 percent confidence interval to estimate the proportion of all residents of the town who approve of the proposal was calculated to be (0.361,⁢0.579).

Which of the following is a correct interpretation of the interval?

• There is a 0.95 probability that the proportion of all residents in the town who favor the proposal will be between 0.361 and 0.579

• The probability that 95 percent of the residents in the town will favor the proposal is between 0.361 and 0.579.

• We are 95 percent confident that the proportion of all residents in the sample who favor the proposal is between 0.361 and 0.579.

• We are 95 percent confident that the proportion of all residents in the sample who favor the proposal is between 0.361 and 0.579.

A random sample of traffic tickets given to motorists in a large city is examined. The tickets are classified according to the race or ethnicity of the driver.The results are summarized in the table. The proportion of this city’s population in each of the racial/ethnic categories is listed in the table. We wish to test 𝐻₀: The racial/ethnic distribution of traffic tickets in the city is the same as the racial/ethnic distribution of the city’s population. Assuming 𝐻₀ is true, what is the expected number of Hispanic drivers who would receive a ticket?

• 8

• 11.84

• 10.36

• 12

• 11

Answer explanation

8% of the population is Hispanic and there was a sample size of 148, so the expected count is 148(0.08).

Inference about the slope 𝛽 of a least-squares regression line is based on which of the following distributions?

• The standard Normal distribution

• The 𝑡 distribution with 𝑛 – 1 degrees of freedom

• The 𝑡 distribution with 𝑛 – 2 degrees of freedom

• The Normal distribution with mean 𝜇 and standard deviation 𝜎

• The chi-square distribution with 𝑛 – 1 degrees of freedom

Answer explanation

There are two variables, so the degrees of freedom is 𝑛 – 2.

Which of the following statements about chi-square distributions are true?

• I, II, and III

• III only

• I and III

• I only

• II only

Answer explanation

Chi-square distributions only take on positive values, so is true. A chi-square distribution with fewer than 10 df is skewed right. It is also true that as the df increases, so does the mean of the distribution.

The mean GPA of students in a course at UCDavis is 3.2 with a standard deviation of 0.3. What percent of students in the course have a GPA between  2.9 and 3.8? 

• 81.5%

• 47.5%

• 68%

• 95%

What percentage of the data is between 90 and 140?

• 25 %

• 50%

• 75%

• 100%