Question 3

The two values between which 95% of the data falls for the average lifespan of a dalmatian are 8.5 years and 14.5 years.

In a normal distribution, approximately 95% of the data falls within two standard deviations from the mean. Given a mean lifespan of 11.5 years and a standard deviation of 1.5 years, the calculation results in a range of 8.5 years to 14.5 years.

A) 10.0 years and 13.0 years

This option is incorrect as it represents a range that does not encompass the full two standard deviations from the mean. The limits of 10.0 years and 13.0 years fall short of the necessary range calculated for 95% of the lifespan data.

B) 9.5 years and 13.5 years

This option is also incorrect as it fails to include the full extent of the two standard deviations. The values of 9.5 years and 13.5 years do not reach the lower limit of 8.5 years and the upper limit of 14.5 years required to capture 95% of the data.

C) 8.5 years and 14.5 years

This option is correct, as it accurately reflects the range within which 95% of the average lifespan data for dalmatians falls. The calculation of mean minus two standard deviations (11.5 - 3.0) gives 8.5 years, and mean plus two standard deviations (11.5 + 3.0) gives 14.5 years.

D) 9.0 years and 14.0 years

This option is incorrect because the range does not include the full two standard deviations from the mean. The limits of 9.0 years and 14.0 years do not extend far enough to encompass the necessary range of 8.5 years to 14.5 years.

Conclusion

The correct answer, 8.5 years and 14.5 years, includes the full range of two standard deviations from the mean lifespan of dalmatians, which is essential for capturing 95% of the data in a normal distribution. All other options fail to meet this criterion, making them incorrect. Thus, C is definitively the right choice.