Question

The lifespans of meerkats in a particular zoo are normally distributed. The average meerkat lives 13.1 years; the standard deviation is 1.5 years. Use the empirical rule to estimate the probability between 16.1 and 17.6 years.

Answer 1

Answer:

The probability between 16.1 and 17.6 years = 0.0214 years

The  Estimate  probability between 16.1 and 17.6 years = 2.14 years

Step-by-step explanation:

Step(i):-

Given the average of Population 13.1 years

The standard deviation of the Population = 1.5 years

Let 'x' be the random variable in Normal distribution

Given x = 16.1

         $Z _{1} = \frac{x- mean}{S.D}$

            $=\frac{16.1-13.1}{1.5}$

           = 2

        Z₁ = 2

Step(ii):-

Given x = 17.6

      $Z_{2} = \frac{17.6- 13.1}{1.5}$

     Z ₂= 3

Z₁ = 2 and    Z ₂= 3 are both positive

The Estimate probability between 16.1 and 17.6 years

P( 16.1<x<17.6) = P( 2 < Z < 3)

                      = A(3) - A(2)

                      =  0.49865 - 0.4772 (from normal table)

                     = 0.0214

The probability between 16.1 and 17.6 years = 0.0214 years

                                                                       =  0.0214 ×100

                                                                      = 2.14 years

Final answer:-

The  Estimate  probability between 16.1 and 17.6 years = 2.14 years

                                                                                           

Answer 2

Answer: 2.35%

Step-by-step explanation: