Question

A really tough trivia quiz has 50 multiple-choice questions, each with four possibleanswers. Use a normal approximation to calculate the probability of randomly guessing the correct answers for at least half of the questions.

Answer 1

Answer:

0.00004

Step-by-step explanation:

Given that:

n = 50

Number of options = 4 ; 1 is the correct answer

Hence ;

p = 1/4 = 0.25

Using normal approximation :

Mean (m) = np = 50 * 0. 25 = 12.5

Standard deviation (s) = √(n*p*q)

q = 1 - p = 1 - 0. 25 = 0.75

s = √(50*0.25*0.75) = 3.062

At least half the question :

Half the question = 1/2 * 50 = 25

P(X ≥ 25) = P(X ≥ 24.5)

(x - m) / s

P(X ≥ 24.5) = (24.5 - 12.5) / 3.062

= 12 / 3.062

= 3.919

P(Z ≥ 3.919) = 0.00004 (Z probability calculator)