Question

Use normal approximation (without continuity correction) to estimate the probability of passing a true/false test of 20 questions if the minimum passing grade is 60% and all responses are random guesses.

Answer 1

This is a binomial distribution question with
n = 20
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 = 12 (60% of 20 = 12)
P(x > 12.0)=?
The z-score at x = 12.0 is,

z = 0.8944
This implies that
P(x > 12.0) = P(z > 0.8944) = 1 - 0.8144
P(x > 12.0) = 0.1856
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