Test Index

NCERT Class XII Mathematics Chapter - - Solutions

© examsnet.com
Question : 64
Total: 101
A class has 15 students whose ages are 14, 17, 15, 14, 21, 17, 19, 20, 16, 18, 20, 17, 16, 19 and 20 years. One student is selected in such a manner that each has the same chance of being chosen and the age X of the selected student is recorded. What is the probability distribution of the random variable X ? Find mean, variance and standard deviation of X
Solution:  
X denote the random variable, which represents the ages of 15 students.
∴ X can assumes values 14, 15, 16, 17, 18, 19, 20, 21
Hence, the probability distribution :
 X  14  15  16  17  18  19  20  21
 P(X)  
2
15
  
1
15
  
2
15
  
3
15
  
1
15
  
2
15
  
3
15
  
1
15
 XP(X)  
28
15
  
15
15
  
32
15
  
51
15
  
18
15
  
38
15
  
60
15
  
21
15
 X2P(X)  
392
15
  
225
15
  
512
15
  
867
15
  
324
15
  
722
15
  
1120
15
  
441
15
Also Mean =ΣXP(X)=
263
15
=17.53 and E(X2)=ΣX2P(X)=
4683
15

σX=√E(X2)−(E(X))2 =√
4683
15
−
69169
225
 =√4.78=2.19
© examsnet.com
Go to Question:
Prev Question
Next Question