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In: Statistics and Probability

(1 point) Use the Normal Approximation to the Binomial Distribution to compute the probability of passing...

(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.

Solutions

Expert Solution

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

please upvote, thanks

orchestra answered 1 year ago
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