A wildlife biologist measures the wingspan, in centimeters, of red-tailed hawks captured at a regional banding station over several consecutive breeding seasons. Based on data from hundreds of previous captures, wingspans in this hawk population are approximately normally distributed with a mean of 132 centimeters and a standard deviation of 6.5 centimeters. One hawk captured during the current season has a wingspan measuring 141.2 centimeters. To the nearest hundredth, what is the z-score corresponding to this hawk's wingspan measurement relative to the population distribution described above?
position: percentiles, z-scores and density curves
Review position: percentiles, z-scores and density curves for AP Statistics and try 2 free AP-style practice questions. 15 questions on this topic in AP Statistics · Unit 1 · Exploring One-Variable Data and Collecting Data.
9 topics174 multiple-choice8 free-response
Try free questions
At a city library the number of books borrowed per month by a cardholder is approximately normally distributed with mean 12 books and standard deviation 4 books. One cardholder borrowed 17 books last month. Which of the following is the standardized score (z-score) of that value?
Sample free-response question
A courier company recorded the delivery times, in minutes, for 10 randomly selected deliveries on each of two routes.
| Route | Delivery times (minutes) |
|---|---|
| North | 12, 15, 15, 16, 18, 19, 21, 22, 24, 38 |
| South | 14, 16, 17, 17, 18, 18, 19, 20, 20, 21 |
(a) Calculate the median delivery time for each route. Show your work.
(b) Is the North delivery time of 38 minutes an outlier? Justify your answer using the 1.5 x IQR rule. The North quartiles are Q1 = 15 and Q3 = 22.
(c) Compare the distributions of delivery times for the two routes. Address center and variability, in context.
(d) The company wants deliveries that rarely take a long time. Which route should it choose? Explain using the comparisons in part (c).
13 more questions on this topic
Full practice for AP Statistics · Unit 1 · Exploring One-Variable Data and Collecting Data: timed tests, step-by-step explanations for every answer, and AI grading for free-response questions.
Start practicing freeInside the course
How practice works on S&D Academy
Answer, then see why
The price of gasoline rises 10% and the quantity demanded falls 5%. What happens to total revenue?
Not quite. The answer is B.
Why the other options are wrong
AI grading for free-response
Write your FRQ answer and get it scored point by point against the AP rubric, with the line from your answer that earned or missed each point.
Question 13 / 4 pts
Part a1 / 1 pts
Point 1: Earned
Grader confidence 94% sureReason: Correctly identifies demand for gasoline as inelastic.
Evidence: "The price of gasoline rises and the quantity falls only a little."
Part b2 / 3 pts
Point 1: Earned
Grader confidence 91% sureReason: Graph shows relatively inelastic demand.
Evidence: Draws a steep demand curve.
Point 2: Earned
Grader confidence 88% sureReason: Correct new equilibrium price.
Evidence: Shifts supply left, P1 → P2.
Point 3: Not earned
Grader confidence 82% sureReason: With inelastic demand, a price increase raises total revenue.
Evidence: "Revenue goes down."