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: $X\sim N(\mu, \sigma^2)$

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

$z=55$

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

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

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