Question

suppose the weight of 800 students are normally distributed with mean 75kg and standard deviation 5kg. find the numer of students that weigh more than 80kg

Answer 1

Let $X=$ the student's weight: $X\sim N(\mu, \sigma^2).$

Given $\mu=75\ kg, \sigma=5\ kg.$

$$P(X>80)=1-P(X\leq 80)$$

$$=1-P(Z\leq\dfrac{80-75}{5} )=1-P(Z\leq 1)$$

$$\approx0.158655$$

$$800(0.158655)=127$$

127 students weigh more than 80kg.