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September 11th, 2011, 04:02 AM   #1
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Finding standard normal random variable

Not really sure how to go about these questions. Any help would be much appreciated

For the standard normal random variable Z, if Pr(Z<-a) = p and a>

a) Pr(Z?a)
b) Pr(-a<Z<a)
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September 11th, 2011, 06:25 AM   #2
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Re: Finding standard normal random variable

Sorry, at first I missed the "Pr(z< -a)= p". Also, since you say this is the standard normal random variable, so the condition is that a> 0.

Pr(Z< 0) is, of course, 1/2, so Pr(-a<= Z<= 0)= 1/2- p. From that, and the symmetry of the Normal distribution, P(0<=Z<= a)= 1/2- p and so Pr(Z<= a)= 1/2- p+ 1/2= 1- p.

And, of course, Pr(-a<= Z<= a)= 2(1/2- p)= 1- 2p, again by symmetry.
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