empirical rule - The lifespans of zebras in a particular zoo are normally distributed the average zebra lives 20.5 years the standard deviation is 3.9 years use the empirical rule to estimate the probability of a zebra living 12.7 and 24.4 years.

Sangeetha Pulapaka (last edited 1 year ago) (Expert, Educator @Qalaxia)

It is given that the lifespans are normally distributed with an average lifespan of 20.5 years.

It is also given that the standard deviation is 3.9 years, so,

one standard deviation above the mean is (20.5 +3.9 =24.4 ) years, two standard deviations above the mean is (24.4 + 3.9 =28.3) years, and three standard deviations above the mean is (28.3+3.9 = 32.2) years.

Similarly one S.D below the mean is 16.6, two S.D's below the mean is 12.7 and three S.D's below the mean is 8.8.

According to the empirical rule, 68% of the data lie within 1 standard deviation of the mean, 95% of the data lie within 2 standard deviations of the mean, 99.7% of the data lie within 3 standard deviations of the mean and 0.3% of the data lie outside the 3 standard deviations from the mean. This is shown in the bell curve below.

So, the probability of a zebra living 12.7 and 24.4 years is 13.5% + 34% + 34% = 81.5%