Question

The weights of 1,000 children, in average, is 49kg with standard deviation of 18kg. Suppose the weights are normally distributed, how many children weigh between 53kg and 59kg?

Answer 1

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

Given $\mu=49 \ kg, \sigma=18\ kg.$

$$P(53<X<59)=P(X<59)-P(X\le 53)$$

$$=P(Z<\dfrac{59-49}{18})-P(X\le \dfrac{53-49}{18})$$

$$\approx P(Z<0.555556)-P(Z\leq 0.222222)$$

$$\approx0.71074264-0.58792955=0.1228$$

$$0.1228(1000)=123$$

123  children weigh between 53kg and 59kg.