Question

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 60% and all responses are random guesses.

Answer 1

Answer)

N = 40

P = 0.5 (as there are two options and only one among those 2, will be correct so probability of getting a correct response is 1/2 = 0.5)

First we need to check the conditions of normality that is if n*p and n*(1-p) both are greater than 5 or not

N*p = 20

N*(1-p) = 20

Both the conditions are met so we can use standard normal z table to estimate the probability

z= (oberved p - claimed p)/standard error

Standard error = √{claimed p*(1-claimed p)/√n

Observed P = 0.6 (60%)

Claimed P = 0.5

N = 40

After substitution

Z = 1.26

From z table, P(z>1.26) = 0.1038