Question

The lifespans of meerkats in a particular zoo are normally distributed. The average meerkat lives 13.113.113, point, 1years; the standard deviation is 1.51.51, point, 5 years.

Use the empirical rule (68−95−99.7%)(68−95−99.7%)left parenthesis, 68, minus, 95, minus, 99, point, 7, percent, right parenthesis to estimate the probability of a meerkat living longer than 14.614.614, point, 6 years.

Answer 1

Let X be the lifespan of meerkats

To find P( X > 14.6 )

X=14.6

That is X =14.6= that is X=14.6  one standard deviation away from mean

P(X> 14.6) =P(X > )

By Emperical rule we know that for a Normal distribution

As total area under Normal curve is 1

As Normal distribution is symmetrical

Thus

P(X> 14.6) =P(X > ) = 0.16

Answer : Probability that a meerkat lives longer than 14.6 years is 0.16