Answer to Question #311804 in Statistics and Probability for May

Question

You volunteered to be a part of the medical mission in your barangay and in charge to get weight of the children. The weight of 1000 children have an average of 45 kilograms and a standard deviation of 5 kilograms. A. How many children weight 35 kg to 55kg.B.How many are in the upper 10% of the population. C. Estimate the range of the number of children weighing.

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

In the upper 10% there will be 0.1*1000=100 kids

It is usually implied that the range of the normal distribution is the difference between mean plus 3 standard deviations and mean minus 3 standard deviations(equal to 6 standard deviations), so i will assume it in that sense. So, the sought range is 6*5 = 30