Question

 Suppose it is known that the weight of a certain population of individuals are approximately normally distributed with a mean 80 kg and a standard deviation of 16 kg. What is the probability that a person picked at random from this group will weight between 60 and 110 kg?

Answer 1

We have a normal distribution, $\mu=80, \sigma=16.$

Let's convert it to the standard normal distribution,

$z=\cfrac{x-\mu}{\sigma}.$

$z_1=\cfrac{60-80}{16}=-1.25;\\ z_2=\cfrac{110-80}{16}=1.88.\\ P(60<X<110)=\\ =P(-1.25<Z<1.88)=\\ =P(Z<1.88)-P(Z<-1.25)=\\ =0.96995-0.10565=\\ =0.8643 \text{ (from z-table)} .$