Question

The marks on a statistics mid-semester exam
are normally distributed with a mean of 78
and a standard deviation of 6.
a What proportion of the class has a mid-
semester mark of less than 75?
b What is the probability that a class of 50
has an average mid-semester mark that is
less than 75?

Answer 1

TOPIC:Normal distribution.

Deling X = Manhs on the statistiee ex am, we need, 75-78 =1(2 <-0.50). N(0, (-0. 50). %3D = 1-(0.50). From No nmat table. = 1- 0.6915. 0. 3085 Here, n = No. of stu dents in the class = 50. 50 -7 X; = sample average. del, 50 Since, the oniginal popu la tion is Nonmal we have, =M =78, o 50 E x N(M= 78, 6 2. 36 50

» Now, we need, >:(R< 19). 75 78 P. 36/50 (z < - 3. 535) P(-3.5355) N (01D. = 1-7(3.5355). Froom Noemat table values, =1- 0.9998 - 0.0002 CAn).