Question

The lifespans of gorillas in a particular zoo are normally distributed. The average gorilla lives 20.8 years; the

standard deviation is 3.1 years.
Use the empirical rule (68 – 95 - 99.7%) to estimate the probability of a gorilla living between 11.5 and 27 years.

Answer 1

If the mean is 20.8, one standard deviation each way is adding and subtracting 3.1, so 17.7 and 23.9 (68% of values)

Two standard deviations adding and subtracting 3.1*2 = 6.2, or 14.6 and 27.

Three standard deviations is 11.5 and 30.1

So we have
11.5 - 14.6 - 17.7 - 20.8 - 23.9 - 27 - 30.1

Going left to 11.5 is 3 standard deviations out, so 99.7/2 = 49.85%

Going right to 27 is 2 standard deviations out, so 95/2 = 47.5%

Add those two % to get 97.32%

This is hard to do without a picture so I hope that helps!