Answer:
0.8508
Step-by-step explanation:
In this question, we are asked to estimate the probability of getting at least 12 correct answers.
X ~ Bin ( n , p)
Where n = 60 , p = 1/4 = 0.25
Mean = np = 60 * 0.25 = 15
Standard deviation = sqrt [ n p ( 1 - p) ] = Sqrt [ 60 * 0.25 ( 1 - 0.25) ] = 3.3541
Using normal approximation
P(X < x) = P(Z < ( x - mean) / SD )
P(X >= 12) = P(X > 11.5)
= P(Z > ( 11.5 - 15) / 3.3541 )
= P(Z > -1.04)
= P(Z < 1.04)
= 0.8508
