AP Statistics · Unit 4 · Probability, Random Variables, and Probability Distributions

77 AP-style multiple-choice questions and 4 free-response questions for AP Statistics · Unit 4 · Probability, Random Variables, and Probability Distributions, sorted into 5 topics. Free sample questions for every topic.

77 multiple-choice4 free-response

Sample free-response question

The transportation office for the Springfield County School District operates 25 bus routes. For a randomly selected school day, let $X$ = the number of routes that are delayed by more than 10 minutes. Based on records from the past 200 school days, the probability distribution of $X$ is partially given below.

$x$	0	1	2	3	4
$P(X=x)$	0.38	0.29	0.18	?	0.05

(a) What is the value of $P(X = 3)$ ? Interpret this value in context.
(b) Calculate and interpret the expected value of $X$ .
(c) District policy states that a new route-monitoring protocol will be implemented if, on more than 30% of school days, at least 2 routes are delayed. What is $P(X \geq 2)$ ? Based on this value, should the district implement the protocol? Justify your answer.
(d) The district has 180 school days in a year. What is the expected total number of route delays for the school year? Interpret this value in context.

Practice AP Statistics · Unit 4 · Probability, Random Variables, and Probability Distributions