Answer to Question #272496 in Statistics and Probability for Semere

Question

The weight of the 5 grade boys is assumed to have normally distributed with mu = 0 kg and sigma = 5 kg find:

The area under the normal curve to the left of point 34kg. What does this area indicate?

Answer 1

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

Given $\mu=50\ kg, \sigma=5\ kg.$ The area under the normal curve to the left of point 34kg indicates the probability that the weight is less than 34 kg

$$P(X<34)=P(Z<\dfrac{34-50}{5})$$

$$=P(Z<-3.2)\approx0.000687$$