Answer to Question #290419 in Statistics and Probability for lusientoo

Question

The weights of 1,000 children, in average, is 50kg with standard deviation of 14kg. Suppose the weights are normally distributed, how many children weigh between 53kg and 68kg?

Answer 1

Let X be a random variable represents the weight of randomly selected child, then X~$N(50,14^2)$

$P(53<X<68)=P(53<N(50,14^2)<68)=P(53<50+14N(0,1)<68)=P(0.214<N(0,1)<1.071)=P(N(0,1)<1.071)-P(N(0,1)<0.214)=0.85792-0.58473=0.27319$

So, approximately 1000*0.27319=273.19=(round to integer)=273 children have such a weight.