AP Statistics · Unit 1 · Exploring One-Variable Data
100 AP-style multiple-choice questions and 10 free-response questions for AP Statistics · Unit 1 · Exploring One-Variable Data, sorted into 5 topics. Free sample questions for every topic.
Sample free-response question
A commercial bakery uses two automated mixing machines, Machine A and Machine B, to produce loaves of artisan bread. A quality-control researcher randomly selects 12 loaves produced by each machine on a given day and records each loaf's weight (in grams). The five-number summaries for the two samples are shown below.
| Machine | Min | Median | Max | |||
|---|---|---|---|---|---|---|
| A | 12 | 430 | 452 | 460 | 470 | 485 |
| B | 12 | 440 | 458 | 478 | 495 | 560 |
A dotplot of Machine A's weights is roughly symmetric and single-peaked, with no unusually high or low values. A dotplot of Machine B's weights is right-skewed, with most loaves clustered between 440 and 500 grams and one noticeably heavy loaf at 560 grams.
(a) Is the heaviest Machine B loaf, 560 grams, an outlier among Machine B's weights? Justify your answer using the rule.
(b) Compare the distributions of loaf weight for Machine A and Machine B.
(c)(i) Suppose each of Machine B's loaf weights is converted from grams to ounces by dividing by 28.35. Explain how this conversion affects the shape, center, and spread of Machine B's distribution of weights.
(c)(ii) Suppose the weights of all loaves produced by Machine A are approximately Normal with mean 460 grams and standard deviation 13 grams. What is the -score of a Machine A loaf that weighs 486 grams? Interpret this -score, and estimate the percentile of the loaf's weight.