The average lifespan of a dalmatian is 11.5 years, with a standard deviation of 1.5 years. What are the two values between which 95% of the data falls for the average lifespan of a dalmatian, assuming a normal distribution?

Rationale

95% of the data for the average lifespan of a dalmatian falls between 8.5 years and 14.5 years.

In a normal distribution, approximately 95% of the data lies within two standard deviations from the mean. Given a mean lifespan of 11.5 years and a standard deviation of 1.5 years, we can calculate the range by subtracting and adding two standard deviations to the mean.

A (10.0 years and 13.0 years) YOUR ANSWER

This range represents only one standard deviation below and one standard deviation above the mean. While it encompasses some of the data, it does not capture the full 95% of the distribution, which requires extending to two standard deviations.

B (9.5 years and 13.5 years) YOUR ANSWER

This choice includes a range that is closer to the mean but still does not reach two standard deviations. The values selected here would only cover about 68% of the data, failing to provide the broader range necessary for 95% coverage.

C (8.5 years and 14.5 years) CORRECT

This choice accurately reflects the calculation of two standard deviations around the mean. Subtracting 3 years (2 times the standard deviation of 1.5 years) from 11.5 years gives 8.5 years, and adding 3 years results in 14.5 years, encompassing 95% of the lifespan data of dalmatians.

D (9.0 years and 14.0 years) YOUR ANSWER

While this range is closer to the mean, it still does not cover the required two standard deviations. It would include more than one standard deviation but not enough to encompass 95% of the data, providing an incomplete representation of the lifespan distribution.

Conclusion

In a normal distribution, the average lifespan of a dalmatian, which is 11.5 years, has a calculated range of 8.5 to 14.5 years for 95% of the data. This range is derived from extending two standard deviations from the mean, ensuring a comprehensive representation of lifespan variability. Other choices either undershoot or do not adequately capture this significant percentage of the data.

The average lifespan of a dalmatian is 11.5 years, with a standard deviation of 1.5 years. What are the two values between which 95% of the data falls for the average lifespan of a dalmatian, assuming a normal distribution?

95% of the data for the average lifespan of a dalmatian falls between 8.5 years and 14.5 years.

Related Questions

Related Quizzes

How familiar were you with this question?

Report an Issue

Rate this Practice Test