A true/false test has 100 questions.Using the normal approximation to the binomial distribution,what is the probability of getting 55 or more correct by just guessing?
A)p(X 55)
B)p(X 55.5)
C)p(X 54.5)
D)p(X 45)

Question

A true/false test has 100 questions.Using the normal approximation to the binomial distribution,what is the probability of getting 55 or more correct by just guessing?​
A)​p(X > 55)
B)​p(X > 55.5)
C)​p(X > 54.5)
D)​p(X > 45)

Quizplus · Accepted Answer

Since we want the probability of getting 55 or more correct, we use the continuity correction and consider the range of 54.5 to 100. We can then use the normal approximation to the binomial distribution with parameters n = 100 and p = 0.5 to calculate the probability as p(X > 54.5) = 1 - P(Z <= (54.5 - np)/sqrt(np(1-p))) = 1 - P(Z <= (54.5 - 50)/sqrt(100(0.5))) = 1 - P(Z <= 1.27) ≈ 0.102. Therefore, the best choice is C, p(X > 54.5).

A True/false Test Has 100 Questions