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Finding standard deviation given proportion?
Random sample of 2 people selected from a group of 5 males and 10 females. Let X be the number of men selected. What is the std. deviation of X?
I made a probability distribution of X=0,1 or 2 but am stuck after that.
P(0boys)=3/7 P(1boy)=2*5/21=10/21 P(2boys)=2/21
Expected boys in a smaple will be 2/3.
std dev= root(n*P*(1-P))
=root(2*.2/3*1*3)
=2/3
AM i doing something right?
1 Answer
- paramvenuLv 73 years ago
Probability distribution of X
X --- P(X)
0 --- 5C0*10C2 / 15C2 = 45/105
1 --- 5C1*10C1 / 15C2 = 50/105
2 ---- 5C2*10C0 / 15C2 = 10/105
Total ------------------------- = 105/105 = 1.00
Mean = E(X) = sigma xp
Variance = sigma x^2p - Mean^2
Standard deviation = sqrt Variance
Mean = sigma xp
= [0*45/105] + [1*50/105] + [2*10/105]
= 0/105 + 50/105 + 20/105
= 70/105 or 2/3
Variance = [0^2*45/105] + [1^2*50/105] + 2^2*10/105] - [2/3]^2
= 0/105 + 50/105 + 40/105 - 4/9
= 90/105 - 4/9
= 6/7 - 4/9
= 54/63 - 28/63
= 26/63
Standard deviation = sqrt [26/63]
= 0.6424
