Answer to Question #292951 in Statistics and Probability for secret

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.