Question

the age in Australia has a normal distribution with mean 45 years and standard deviation 11 years. the children are classified as the youngest 33% of population. at what age do children become adults in Australia

Answer 1

Let X be age of children in Australia.

X has a normal distribution with mean µ = 45 years and standard deviation σ = 11 years.

We want to find at what age do children become adults in Australia.

We have given that the children are classified as the youngest 33% of population.

Let consider the C be the age that children do become adults in Australia.

That means the age of children less than C are 33%.

P(X ≤ C) = 0.30

The below 33% of children have age is below C years.

We will solve this problem by standardizing.

P(X ≤ C) = P ((X - µ)/σ < (C – 45)/11) = P(Z < (C – 45)/11)

P(Z ≤ (C – 45)/11) = 0.33

The Z score to corresponding area is 0.33 is -0.44(using statistical table).

(C – 45)/11 = -0.44

C = -0.44*11 + 45

C = 40.16

At age 40 children become adults in Australia.