Answer to Question #333520 in Statistics and Probability for Brizhel

Question

The weight of 1000 children average 50 kg and the standard deviation is 5kg. What is the Area under the normal curve that corresponds to the z-score of 55

kg?

Answer 1

Let $X$ be a random variable denotes the children's weight: $X\sim N(\mu, \sigma^2)$

$$Z=\dfrac{X-\mu}{\sigma}\sim N(0, 1)$$

$z=55$

$$P(Z=55)=0$$

$$P(Z<55)=P(Z\le 55)\approx1$$

$$P(Z>55)=P(Z\ge 55)\approx0$$