Question

If the results of an examination have a normal distribution with a mean of 78 and σ = 36 a) What is the probability that a person will obtain a grade higher than 72? b) What should be the minimum passing grade, if the teacher intends that only 28.1% of the students pass (percentage of the right tail)? Write your answer as XX.XX c) What must be the minimum passing grade for only 20% to pass the exam (percentage of the left tail)? . Write your answer as XX.XX

Answer 1

a) P(X > 72)

= P(z > (72 - 78)/36)

= P(z > -0.17)

= 0.5675

b) z score for top 28.1% area = 0.58

Hence,

Minimum passing grade required = 78 + 0.58 * 36 = 98.88

c) z score for top 20% = 0.84

Hence,

Minimum passing grade = 78 + 0.84 * 36 = 108.24