Answer to Question #292950 in Statistics and Probability for secret

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.