Question

the lifespans of lions in a particular zoo are normally distributed. the average lion lives 10 years; the standard deviation is 1.4 years. use the empirical rule (68 - 95 - 99.7%) to estimate the probability of a lion living between 7.2 and 11.4 years.

Explanation:

Step1: Calculate number of standard - deviations from the mean

For the lower value: $\frac{10 - 7.2}{1.4}=\frac{2.8}{1.4} = 2$ standard - deviations below the mean.
For the upper value: $\frac{11.4 - 10}{1.4}=\frac{1.4}{1.4}=1$ standard - deviation above the mean.

Step2: Apply the empirical rule

The empirical rule states that about 68% of the data is within 1 standard - deviation of the mean, about 95% is within 2 standard - deviations of the mean.
The area within 2 standard - deviations of the mean is 95% (from - 2 to 2 standard - deviations), and the area within 1 standard - deviation of the mean is 68% (from - 1 to 1 standard - deviations).
The area between - 2 and 1 standard - deviations is $\frac{95 + 68}{2}=81.5\%$.

Answer:

81.5