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Fynjy0 [20]
4 years ago
7

A math exam has 44 multiple choice questions, each with choices a to d. One student did not study and must guess on each questio

n. 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.
Mathematics
1 answer:
jenyasd209 [6]4 years ago
6 0

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

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