3D-Printing Club: Test a Tumbling Part

Use repeated trials to estimate landing probabilities and plan future tests.

Build the Trial Record

The club designs a 3D-printed tumbling part for a moving model. Use the recorded trials to estimate its landing probabilities.

The part can settle on its broad base, narrow base, or side. These are the only recorded outcomes. For each trial, students shake the same part in a cup, release it from a marked height onto the same padded tray, and wait for it to stop. They keep this procedure unchanged.

During one release, the part touches its broad base, rolls, and finally rests on its side. How should this trial be recorded?

A. Record one broad-base result and no side result.B. Record no result and repeat the release instead.C. Record one side result and no broad-base result.D. Record one broad-base result and one side result.

First Session: Separate Blocks of Trials
Block	Releases	Broad-base landings
1	50	26
2	50	33
3	50	28
4	50	29

What is the relative frequency of broad-base landings in Block 2? Write a decimal.

Using all four blocks, estimate the probability of a broad-base landing. Write a decimal.

After a fifth block of 50 releases, the broad-base relative frequency for all 250 releases is 0.60.

How many broad-base landings occurred in the fifth block? landings

The four original blocks have broad-base relative frequencies of 0.52, 0.66, 0.56, and 0.58. Which conclusion is supported?

A. Separate blocks can have different relative frequencies under the same procedure.B. Different relative frequencies prove that students changed the trial procedure.C. The most recent block determines the exact probability for all future trials.D. Every future block must have a relative frequency between 0.52 and 0.66.

Use a Longer Test

Use only the new session below for Questions 6–10. Keep predictions approximate, even when the calculated count is a whole number.

New Session: 400 Releases Under the Same Procedure
Final resting position	Number of releases
Broad base	232
Narrow base	60
Side	108

Estimate the probability of a narrow-base landing. Write a decimal.

For a model demonstration, either a broad-base landing or a side landing counts as a usable result.

Estimate the probability of a usable result. Write a decimal.

The club plans to film 300 more releases using the same procedure. Use the new session's side-landing relative frequency.

About how many side landings should the club predict? side landings

An animation project needs footage of 150 broad-base landings. The club can film 250 releases. Use 232/400 as the estimated broad-base probability.

By how many landings is the predicted broad-base count below the goal? landings

10.

Using the new session, the club predicts about 24 narrow-base landings in 160 future releases. Which statement correctly interprets this prediction?

A. Exactly 24 narrow-base landings must occur if the procedure stays unchanged.B. At least 24 narrow-base landings must occur if the procedure stays unchanged.C. Exactly 24 narrow-base landings must occur in each separate group of 160.D. The actual narrow-base count may be above or below 24 in those releases.

Evaluate the Evidence

Consider how more trials and complete records affect a probability estimate.

11.

The club continues the 400-release session for another 100 releases. These additional releases produce 64 broad-base landings. Update the estimate using all 500 releases.

What is the updated broad-base relative frequency? Write a decimal.

12.

Asha keeps testing the unchanged part using the same procedure. Select every statement that correctly describes relative frequency over many trials.

13.

A redesigned part has no narrow-base landings in its first six releases. What is the best next step before treating its narrow-base probability as zero?

A. Declare narrow-base landings impossible because none occurred yet.B. Run many more releases and record every final resting position.C. Record only broad-base landings during the next trial session.D. Assign each resting position probability 1/3 without more tests.

14.

Eli tests another printed part. Whenever it lands on its side, he deletes that result and releases it again. He uses only the remaining broad-base and narrow-base landings to estimate the probability of a broad-base landing on a single release. Explain why his estimate is misleading and describe how to fix the record.