Re: Normal Distribution

REVISED ANSWER


There is some thing called CENTRAL LIMIT THEOREM which talk about this
Total mean = 17+13+13 = 43
Total variance= 2^2+1^2+2^2 = 4+4+1=9
Hence s.d.=9^1/2 = 3
Hence the new the p.d.f for this normal distribution is
= (1/s.d .(2 pi) ^ 1/2) * e^[(x - mean)/2(s.d)^2]
=(1/3 .(2 pi) ^ 1/2) * e^[(x -43/2(3)^2]
and
P(X<=40) =P((X-43)/3<(40-43)/3) = P(z <
-.1)=P(z>1)=1-P(z<1)=1-.3413=.6587

where z is standard normal variable

Let me know the feed back.

.