Question

In a sample of 100 students, the mean of the marks (only integers) obtained by them in a test is 14 with its standard deviation of 2.5 (marks obtained can be fitted with a normal distribution). The percentage of students scoring 16 marks is

(Area under standard normal curve between z = 0 and z = 0.6 is 0.2257; and between z = 0 and z = 1.0 is 0.3413)

• A. 36
• B. 23
• C. 12
• D. 10

Answer 1

The correct option is B 23

N = 100 students,
For single student, x = {marks obtained}

${\mu }_x=14,{\sigma }_x=2.5$

$z_x=\frac{x-{\mu }_x}{{\sigma }_x}=\frac{16-14}{2.5}=\frac{2.0}{2.5}=0.8$

$P(X\le 16)=P(z<0.8)$ = lies between 0.2257 to 0.3413 (According to question).

So % of students getting marks less than 16 = between 22% to 34%.

So only option satisfying it = 23%