Question

Suppose that the birth weight of babies X has a normal distribution with mean µ = 2.4 kg, and standard deviation σ =0.5 kg. A baby chosen at random. Find The birth weight C if PX>x=0.60.

Answer 1

$X\sim N(\mu, \sigma^2)$

Then

$$Z={X-\mu \over \sigma}\sim N(0,1)$$

Given that $\mu=2.4\ kg, \sigma=0.5\ kg$

$P(X>x)=0.60$

$$P(X>x)=1-P(X\leq x)=1-P(Z\leq {x-2.4 \over 0.5})=0.60$$

$$P(Z\leq {x-2.4 \over 0.5})=1-0.60=0.40$$

$${x-2.4 \over 0.5}\approx-0.253348$$

$$x\approx0.5(-0.253348)+2.4\approx2.2733$$

$\text{Birth weight}=2.2733\ kg$