Question

The weights of students in a certain school are normally distributed with a mean weight of 66 kg. 10% have a weight greater than 70kg. What percentage of students weighs between 52kg and 66kg?   

Answer 1

$P(X>70)=0,1;\\ P(X<70)=1-0.1=0.9.$

The closest to 0.9 value in the z-table is 0.8997 for z=1.28.

$z=\cfrac{x-\mu}{\sigma},\\ \sigma=\cfrac{x-\mu}{z}=\cfrac{70-66}{1.28}=3.125;$

$z_1=\cfrac{52-66}{3.125}=-1.92;\\ z_2=\cfrac{66-66}{3.125}=0;\\ P(52<X<66)=P(-1.92<Z<0)=\\ =P(Z<0)-P(Z<-1.92)=\\ =0.5000-0.0274=0.4726 \text{ (from z-table).}$