Question

The lifespans of seals in a particular zoo are normally distributed. The average seal lives 13.8 years; the standard deviation is 3.2 years. Use the empirical rule (68-95-99.7) to determine the percentage of seals that live between 10.6 and 17 years?

Answer 1

Using the empirical rule, it is determined that approximately 68% of the seals live between 10.6 and 17 years, since this range is within one standard deviation of the mean lifespan.

Step-by-step explanation:

The student's question pertains to the use of the empirical rule (also known as the 68-95-99.7 rule), which applies to normally distributed data. The empirical rule states that roughly 68% of data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. Given that the average lifespan of seals is 13.8 years with a standard deviation of 3.2 years, we can calculate the lifespan range that falls within one standard deviation of the mean (from 10.6 to 17 years).

To find the percentage of seals living between 10.6 and 17 years, we note that this range encompasses the mean plus or minus one standard deviation (13.8 ± 3.2 years). Therefore, according to the empirical rule, we expect approximately 68% of the seals to have lifespans within this range.