Question

The final exam scores in a statistics class were normally distributed with a mean of 70 and a standard deviation of five. What is the probability that a student scored more than 75% on the exam?

Answer 1

X : Final exam score

X follows normal distribution with mean: = 70 and standard deviation : = 5

Probability that a student scored more than 75% on the exam = P(X>75)

P(X>75) = 1- P(X75)

Z-score for 75 = (75-)/ = (75-70)/5 = 1

From standard normal tables P(Z1) = 0.8413

P(X75) = P(Z1) = 0.8413

P(X>75) = 1- P(X75) = 1-0.8413 = 0.1587

Probability that a student scored more than 75% on the exam = P(X>75) = 0.1587

Ans:

Probability that a student scored more than 75% on the exam = 0.1587