Answer to Question #290584 in Statistics and Probability for mercy

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.