Question

A math exam has 44 multiple choice questions, each with choices a to d. One student did not study and must guess on each question. Normal approximation is used to estimate P(12 correct). This value will be different than the exact value computed by the binomial distribution. Find P(12 correct) by normal approximation to the binomial.

Answer 1

Answer:

Step-by-step explanation:

Given that a math exam has 44 multiple choice questions, each with choices a to d.

A student answers just by guessing.  So no of questions he answers X is binomial with constant probability 1/4 = 0.25

We can find probabibility using binomial as

P(X=12) =$44C12 (0.25)^{12} (0.75)^{32} \\=0.1263$

If approximated to normal we have

mean = np = 11

Std dev = $\sqrt{npq} \\=2.873$

With continuity correction we get

P(X<12)

=P(X<11.5)

=0.5691