Difficulty: Hard

Average Score: 42%

A kneepad manufacturer tested a new kneepad design for use in industrial settings. In order to be rated for the intended use, the kneepads each needed to withstand a force of 100 newtons (N) on the outside of the kneepad without distorting the inside by more than 5 millimeters. During testing, the force on each kneepad was steadily increased until the kneepad failed. The table shows the manufacturer's results from testing 100 of the kneepads.

If these results correctly predict the performance of this kneepad design, what is the probability that one of the kneepads will require a force of 145 N or greater to cause failure?

Rationale

The probability that one of the kneepads will require a force of 145 N or greater to cause failure is 25%.

This probability indicates that, based on the performance predictions of the kneepad design, there is a one in four chance that a kneepad will fail under a force of 145 N or more.

A (53%) YOUR ANSWER

This choice suggests that more than half of the kneepads would fail under the specified force, which is inconsistent with the given data. A probability of 53% would imply a significantly higher likelihood of failure than what the performance predictions indicate.

B (22%) YOUR ANSWER

A probability of 22% indicates that there is a lower chance of failure than the actual prediction. This does not align with the 25% probability stated, and it underrepresents the likelihood of failure under the specified force.

C (75%) YOUR ANSWER

Choosing 75% would imply that the vast majority of kneepads are likely to fail when subjected to the force of 145 N. This is an exaggerated assessment and contradicts the prediction of only a 25% chance of failure, suggesting a misunderstanding of the data provided.

D (25%) CORRECT

This accurately reflects the predicted data regarding the kneepad design, indicating that 25% of the kneepads are expected to require a force of 145 N or greater to fail. This aligns perfectly with the performance evaluation criteria set forth in the problem.

Conclusion

The assessment of the kneepad design's performance reveals a 25% probability of failure when subjected to a force of 145 N or greater. This aligns with the experimental predictions, distinguishing it from the other options that either significantly overestimate or underestimate the likelihood of failure. Understanding this probability is crucial for evaluating the reliability and safety of the kneepad design in practical applications.

If these results correctly predict the performance of this kneepad design, what is the probability that one of the kneepads will require a force of 145 N or greater to cause failure?

The probability that one of the kneepads will require a force of 145 N or greater to cause failure is 25%.

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