Question

A multiple choice quiz has 400 questions, each question with five possible answers of which one is correct answer. What is the probability that a sheer guess yields exactly 80 correct answers using normal approximation.  

Answer 1

$X~$~ bin(n, p)

where,

n= 400

p= 1/5 = 0.2

q = 1- p = 0.8

We can say that the sampling distribution of X can be approximately normal with :

mean = $np=(400\times 0.2)=80$

Standard deviation $sd=\sqrt{npq}=\sqrt{400\times 0.2\times 0.8}=8$

Now, the probability that a guesswork yields exactly 80 correct answers is :

$=P(X=80)\\=P(79.5\leq X\leq 80.5)$

$\approx 0.0498$ [TI84 function : normalcdf (79.5,80.5,80,8) ]