Answer to Question #198979 in Statistics and Probability for Ubaid

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

We have given that,

$n = 400$

$p = \dfrac{1}{5} = 0.2$

$q = 0.8$

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

Mean $= np = 400 \times 0.2 = 80$

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

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

$P(X = 80)$

$= P(79.5\le X\le80.5)$

$= 0.049$