AP Statistics Practice Exam 1: Free Response

Section II · 4 questions · 90 minutes · math parts marked line by line · scoring guide for the rest

▶ Section I: multiple choice 🖨 Print the exam Answers and scoring guide

How it works

Free response: 4 questions, 10 points each, 90 minutes, graphing calculator.
On the real exam you type your answers in the Bluebook app. Each question is worth 10 points.
Math parts (✎): type your working one line at a time. When the section ends, every line is marked like an exam: working marks for right lines, the last mark for the right answer.
Parts that need words, a reason or a drawing: write your answer, then, after the section, open our solution and its scoring guide and tick the points your answer earns.
At the end: your section II points, and with section I your AP score estimate (1-5).

Your written answers are kept in this browser. No sign-up.

Question 1: Does a reading app help? (10 points)

A school with 600 students wants to know whether a new reading app makes students read faster. 40 students volunteer. The school will measure each volunteer's reading speed (words per minute) after one month.

(a) Write an investigative question that this study could answer. (2 points)
(b) Describe how to assign the 40 volunteers at random to two groups of 20: one uses the app, one does not. (3 points)
(c) Why is it important to assign the students at random? (2 points)
(d) The 40 students are volunteers, not a random sample of the school. How does this limit the conclusions? Describe one way the volunteers may be different. (3 points)

Question 2: Hours of sleep (10 points)

A random sample of 8 students at a college reported their hours of sleep last night: 6, 7, 8, 5, 9, 7, 6, 8.

(a) Find the mean of the 8 values. (2 points)
(b) Find the sample standard deviation of the 8 values, to one decimal place. (3 points)
(c) Find the median and the quartiles. Describe the shape of the distribution. (2 points)
(d) Another student slept 10 hours. Find the z-score of 10 hours using your answers to (a) and (b), and say what it means. (3 points)

Question 3: Biking to work (10 points)

A town says that 30% of its working residents bike to work. In a random sample of 200 working residents, 75 bike to work. Is there convincing evidence, at the 5% level, that more than 30% of the town's working residents bike to work?

(a) State the hypotheses and say what the parameter is. (2 points)
(b) Check the conditions for a one-sample z-test for a proportion. (2 points)
(c) Find the test statistic and the p-value. (4 points)
(d) State your conclusion in context. (2 points)

Question 4: Checking items at a factory (10 points)

At a factory, each item from a machine needs a second check with probability 0.3, independently of other items. The weights of the items are normal with mean 70 grams and standard deviation 6 grams.

(a) 8 items are picked. Find the probability that exactly 2 of them need a second check. (3 points)
(b) For 8 items, find the mean and the standard deviation of the number that need a second check. (2 points)
(c) Find the probability that one item weighs more than 80 grams. (3 points)
(d) Two items are picked. Find the probability that both weigh more than 80 grams. What do you have to assume? (2 points)

Steply AP practice exams are our own questions, written in the style of the AP exams for May 2027; they are not official, and the AP score is our own rough estimate. AP® is a trademark registered by the College Board, which is not affiliated with, and does not endorse, this site. Official practice: the College Board's AP Students site and its free-response questions from past years.