A class has 15 students whose ages are 14,17,15,14,21,17,19,20,16,18,20,17,16,19 and 20 yr. One students is selected in such a manner that each has the same chance of being of chosen and the age X of the selected stuydent is recorded. Mean variance and standard deiation (SD) of X,are respectvely

Options

A. 17.53,4.8 and 2.19
B. 2.19, 4.8 and 17.53
C. 17.53,2.19 and 4.8
D. None of these

Answer

A

Explanation

Here, total number of students = 15
The ages of students in ascending order are 14,14,15,16,17,17,17,18,19,19,20,20,21
Now, `P(X=14)=2/(15),P(X=15)=1/(15)`
`P(X=16)=2/(15),P(X=17)=3/(15)`
`P(X=18)=1/(15),P(X=19)=2/(15)`
`P(X=20)=3/(15),P(X=21)=1/(15)`
Therefore, the probability distribution of randon variable X is as follows
The third row gives the probability distribution of X
Mean of `X=SigmaXP(X)`
`=(14xx2+15xx1+16xx2+17xx3+18xx1+19xx2+20xx3+21xx1)/(15)`
`=(28+15+32+51+18+38+60+21)/(15)=(263)/(15)=17.53`
Variance `X=SigmaX^2P(X)-("Mean")^2`
`([(14)^2xx2+(15)^2xx1+(16)^2xx2+(17)^2xx3+(18)^2xx1+(19)^2xx2+(20)^2xx3+(21)^2xx1])/(15)-((263)/(15))^2`
`=(392+225+512+867+324+722+1200+441)/(15)-((263)/(15))^2`
`=(4683)/(15)-((263)/(15))^2=312.2-307.4=4.8`
`"SD of X"=sqrt("Variance")=sqrt(4.8)=2.19`