Answer to Question #310914 in Statistics and Probability for Butchuy

Question

You volunteered to be part of the medical mission in your barangay and in-charge to get weight of the children. The weights of 1,000 children have an average of 45 kilograms and a standard deviation of 5 kilograms.

a. How many children weigh 35 kg to 55 kg?

Answer 1

Let X be a random variable representing the weight of the children, then X ~ $N(45,5^2)$

$P(35<X<55)=P(35<N(45,5^2)<55)=P(35<45+5N(0,1)<55)=P(-2<N(0,1)<2)=2P(0<N(0,1)<2)=2*0.47725=0.9545$

So, among the 1000 children there will be approximately 1000*0.9545=954.5 $\approx$ 955 with such weight