Question

The weights of 1,000 children, in average, is 61kg with standard deviation of 10kg. Suppose the weights are normally distributed, how many children weigh less than 60kg?

Answer 1

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

Given $\mu=61 \ kg, \sigma=10\ kg.$

$$P(X<60)=P(Z<\dfrac{60-61}{10})$$

$$=P(Z<-0.1)\approx 0.460172$$

460 children weigh less than 60kg.