A multiple choice test 30 questions, and each question has 5 answer choices (exactly one of which is correct). A student taking the test guesses randomly on all questions. Using the Normal approximation with continuity correction, determine the approximate probability that the student will get at least as many correct answers as he would expect to get with the random guessing approach.

Question

Mathematics

Cael Lyons

24 June, 20:41

A multiple choice test 30 questions, and each question has 5 answer choices (exactly one of which is correct). A student taking the test guesses randomly on all questions. Using the Normal approximation with continuity correction, determine the approximate probability that the student will get at least as many correct answers as he would expect to get with the random guessing approach.

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Kaitlynn Harding · Answer 1

Step-by-step explanation:

Given that a multiple choice test 30 questions, and each question has 5 answer choices (exactly one of which is correct).

When a student taking the test guesses randomly on all questions, p for success in each trial = 1/5 = 0.2

As there are two outcomes and each event is independent of the other

X no of correct questions is binomial with n = 30 and p = 0.2

If approximated to normal

mean=np = 15 and Variance = np (1-p) = 4.8

Std dev = 2.191

X is normal (15, 2.191)

His expected value = mean = np

Required prob = P (X>15) = P (X>14.5) using continuity correction

=P (Z>-0.5/2.191) = P (Z>-0.23) = 0.5910