Question

Questions 28 and 29 are related
28	A large number of students took a departmental math test, of whom 6 percent scored 90 or more from the scale of 100. The scores have a bell-shaped distribution with a standard deviation of 8. If the minimum score to pass the test is 60, what fraction of the students failed the test?
a	0.0307
b	0.0228
c	0.0139
d	0.0096
29	The middle interval which includes 95% of the test scores is _______ to _______.   (Round the scores to the nearest integer.)
a	66	90
b	65	91
c	64	92
d	62	93

Answer 1

Solution:-

28) (c) The fraction of the students failed the test is 0.0139.

S.D = 8

x_top6% = 90

p-value for the top 6% = 0.94

z-score for the p-value = 1.555

By applying normal distruibution:-

x = 60

By applying normal distruibution:-

z = - 2.195

P(z < - 2.195) = 0.014

29) (d) The middle interval which includes 95% of the test scores is 62 and 93.

C.I = 77.56 + 1.96 × 8

C.I = 77.56 + 15.68

C.I = (61.88, 93.24)