Answer to Question #230149 in Statistics and Probability for James

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

Since $np=1500*0.2=300>5$ and $n(1-p)=1500*0.8=1200>5$, we can use the normal approximation to the binomial to solve a problem.

For this approximation $\mu=np=300, \;\sigma=\sqrt{np(1-p)}=\sqrt{240}\approx15.49.$

$P(X>100)=P(Z>\frac{100-300}{15.49})=P(Z>-12.91)=1-P(Z<-12.91)=$

$=1-1.98*10^{-38}.$