Z SCORE AND PROBABILITIES

Question

1.     A large chemistry course took their final exam. The mean was 75 with a standard deviation of 8.

a.      What are the exam scores that separate the top and bottom 5 percent of the class (extreme 10%)?

b.     What are the exams scores that separate the middle 10% of the class (5% on each side of the mean)?

c.      What proportion of people scored in the A range (90 or above)

d.     What proportion of people failed the exam (60 or below)?

Answer 1

mean = 75, standard deviation = 8

by the empirical rule, 90% of the scores fall within 2 standard deviations from the mean

75+/-2(8) = 75+/-16= 91 and 59 both which have z scores=2

the top 5% is above 91

the bottom 5% is below 59

z scores for middle 10% are found in z tables or a z calculator. set (75-x)/8 = z =.125 and solve for x

75-x = .125(8) = 1

x =74

the middle 10% are approximately between 74 and 76

(90-75)/8 = 15/8 = 1.875 = z

use z tables or a z calculator to find the area under the curve = percentage