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 September 11th, 2011, 03:02 AM #1 Newbie   Joined: Apr 2010 Posts: 24 Thanks: 0 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>µ Find: a) Pr(Z?a) b) Pr(-a
 September 11th, 2011, 05:25 AM #2 Math Team   Joined: Sep 2007 Posts: 2,409 Thanks: 6 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, $\mu= 0$ 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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