Situation: You volunteered to be part of the medical mission in your barangay and in-charge to get weight of the children. The weights of children have an average of kilograms and a standard deviation of kilograms. a. How many children weight 35 kg to 55 kg? b. How many are in the upper 10% of the population? c. Estimate the range of the number of children weighing c.1. 40kg to 50kg c.2. below 55kg c.3. between 25kg to 58kg

Let $X=$ weight of children: $X\sim N(\mu, \sigma^2)$

Given $\mu=45kg, \sigma=5kg$

a.

$P(35<X<55)=P(X<55)-P(X\le35)$

$=P(Z<\dfrac{55-45}{5})-P(Z\le\dfrac{35-45}{5})$

$=P(Z<2)-P(Z\le-2)$

$\approx0.97725-0.02275=0.9545$

b.

$1-P(Z\le\dfrac{x-45}{5})=0.1$

$\dfrac{x-45}{5}\approx1.28155$

$x\approx51.408$

c.

c.1.

$P(40<X<50)=P(X<50)-P(X\le40)$

$=P(Z<\dfrac{50-45}{5})-P(Z\le\dfrac{40-45}{5})$

$=P(Z<1)-P(Z\le-1)$

$\approx0.84134-0.15866=0.6827$

c.2.

$P(X<55)=P(Z<\dfrac{55-45}{5})$

$=P(Z<2)\approx0.97725$

c.3.

$P(25<X<58)=P(X<58)-P(X\le25)$

$=P(Z<\dfrac{58-45}{5})-P(Z\le\dfrac{25-45}{5})$

$=P(Z<2.6)-P(Z\le-4)$

$\approx0.99534-0.00003=0.9953$