The average commute time for workers in a city in 2021 was 35 minutes, with a standard deviation of 5 minutes. Assuming a normal distribution, which two values encompass 95% of the data?

Rationale

25 minutes and 45 minutes encompass 95% of the data.

In a normal distribution, approximately 95% of the data falls within two standard deviations of the mean. With a mean commute time of 35 minutes and a standard deviation of 5 minutes, this range would extend from 25 minutes (35 - 2*5) to 45 minutes (35 + 2*5).

A (25 minutes and 45 minutes) CORRECT

This choice correctly identifies the interval that captures 95% of the data in a normal distribution. The mean of 35 minutes, minus and plus two standard deviations (10 minutes total), yields a lower bound of 25 minutes and an upper bound of 45 minutes, effectively encompassing the majority of commute times.

B (30 minutes and 40 minutes) YOUR ANSWER

While this range is close to the mean, it only spans 10 minutes (a single standard deviation from the mean). Therefore, it captures approximately 68% of the data, not the 95% indicated in the question. This range is insufficient for representing the broader distribution of commute times.

C (35 minutes and 40 minutes) YOUR ANSWER

This choice includes the mean but only extends slightly above it. Like option B, it captures a narrow range of 5 minutes, which represents even less than the 68% of data typically included within one standard deviation of the mean. It fails to encompass the required 95% of values.

D (20 minutes and 50 minutes) YOUR ANSWER

This range exceeds the necessary boundaries for 95% of the data. Although it does capture more than 95% of the data, it is not the most accurate or precise interval according to the 68-95-99.7 rule, which specifically defines the limits as being within two standard deviations from the mean.

Conclusion

Understanding the properties of a normal distribution is crucial for accurately interpreting statistical data. The correct range of 25 minutes to 45 minutes encapsulates 95% of workers' commute times in this scenario, demonstrating the efficacy of the 68-95-99.7 rule in applied statistics. Options that do not adhere to this principle either under-represent or over-represent the data, highlighting the importance of precise calculations in statistical analysis.

The average commute time for workers in a city in 2021 was 35 minutes, with a standard deviation of 5 minutes. Assuming a normal distribution, which two values encompass 95% of the data?

25 minutes and 45 minutes encompass 95% of the data.

Related Questions

Related Quizzes

How familiar were you with this question?

Report an Issue

Rate this Practice Test