Question

(1 point) Use the Normal Approximation to the Binomial Distribution to compute the probability of passing a true/false test of 40 questions if the minimum passing grade is 90% and all responses are random guesses.

Answer 1

This is a binomial distribution question with
n = 40
p = 0.5
q = 1 - p = 0.5
This binomial distribution can be approximated as Normal distribution since
np > 5 and nq > 5
Since we know that


x = 0.9*40 = 36

This implies that


The probability of passing a true/false test of 40 questions if the minimum passing grade is 90% and all responses are random guesses is ZERO as the deviation between mean and 'x' is more than 3 standard deviation

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