The weights of 1,000 children, in average, is 62kg with standard deviation of 19kg. Suppose the weights are normally distributed, how many children weigh greater than 56kg?

Solution:

Given : mean= 62

sd = 19

formula Z= $\frac{x-mean}{sd}$

For x= 56, Z= $\frac{56-62}{19}=-0.32$

Using Z table , Pr(X>56) = Pr(Z$>$ −0.32)=Pr(Z$\le$ 0.32)=0.62552

Hence number of children = 1000$\times$ 0.62552= 625.52 approximately 626 children