Question

The mean score on the test in Sociology 2205 last year was 52 with a standard deviation of 5. Assuming the test scores are normally distributed, answer the following questions. (You do not need to show any of your calculations.) (ANSWER IN WORDS ONLY PLEASE)

(a) Raffi scored 45 on the examination. What is his percentile score?

(b) Freya wrote the same test and scored 54. How many individuals scored higher than she did?

(c) Anthony’s percentile score on the same test was 92. What was his actual score?

Answer 1

solution:

the mean score = = 52

standard deviation = = 5

a)

score of Raffi = X = 45

z score for X = 45,

P(X < 45) = value of z to the left of -2 from the z table = 0.0228

so percentile score for Raffi = 2.28th percentile.

b)

Freyas score = X = 54

P(X > 54) = 1 - value of z to the left of -0.2 = 1 - 0.4207 = 0.5793

number of students score higher than Freya = 57.93%

c)

percentile score of anthony = 92th

so z score with 0.92 area to the left of distribution = 1.41

so Anthony's score will be approximately = 62.05