Answer to Question #229866 in Statistics and Probability for Eugine

Question

The incidence of COVID 19-disease at Rusangu university is such that on the average twenty percent of students suffer from it. If 1500 students are selected at random, what is the chance that more than 100 students suffer from COVID 19-disease

Answer 1

Let $X=$ the number of students suffered from COVID 19-disease: $X\sim Bin(n, p).$

Given $n=1500, p=0.2.$

Use the Normal Approximation to the Binomial Distribution: $X\sim N(np, npq).$

$$P(X>100)=1-P(X\leq100)$$

$$=1-P(Z\leq\dfrac{100-1500(0.2)}{\sqrt{1500(0.2(1-0.2))}})$$

$$\approx1-P(Z\leq-12.90994449)\approx1$$