Question

forty students took a test on which the mean score was an 82 and standard deviation was 7.8. the distribution of the scores followed a normal model and a grade of B or better was assigned to all students who scored 85 or higher. approximately how many grades of B or better were given? (choose closest answer) (a) 8, (b) 10, (c) 14, (d) 28, (e) 35

Answer 1

Solution:

Given, the Normal distribution with,

   = 82

= 7.8

First we find the probability of getting B grade .

Probability

= P(X > 85)

= P[(X - )/ >  (85- )/]

= P[Z > (85 - 82)/7.8]

= P[Z > 0.38]

= 1 - P[Z < 0.38]

=    1 - 0.648 ( use z table)

=    0.352

Now ,

n = 40

p = 0.352

approximately how many grades of B or better were given?

Answer = n * p = 40 * 0.352 = 14

Option C is correct.