Answer to Question #230726 in Statistics and Probability for Solomon

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-diseas

Answer 1

$np=1500 \times 0.2 = 300 > 5 \\ n(1-p) = 1500 \times 0.8 = 1200 >5$

So, we can use the normal approximation to the binomial to solve a problem.

For this approximation

$\mu=np=300 \\ \sigma = \sqrt{np(1-p)} = \sqrt{240}=15.49 \\ P(X>100) = 1 -P(X≤100) \\ = 1 -P(Z≤ \frac{100-300}{15.49}) \\ = 1 -P(Z≤ -12.91) \\ = 1-1.98 \times 10 ^{-38}$