Question

A student is taking a true/false exam with 17 questions. If he guesses on each question, what is the probability he will get at least 14 questions correct?

Answer 1

X ~ Bin ( n , p)

Where n = 17 , p = 0.5

np = 17 * 0.5 = 8.5

n(1-p) = 17 * 0.5 = 8.5

Since np > 5 and n( 1 - p) > 5, normal approximation is appropriate.

Mean = n p = 17 * 0.5 = 8.5

Standard deviation = sqrt [ n p ( 1 - p) ]

= sqrt [ 17 * 0.5 * 0.5 ]

= 2.0616

Using normal approximation,

P(X < x) = P(Z < ( x - Mean) / SD)

With continuity correction,

P(X >= 14) = P(Z > (13.5 - 8.5) / 2.0616 ) [ With continuity correction , P(X >= x) = P(X > x-0.5) ]

= P(Z > 2.43 )

= 0.0075