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September 11th, 2011, 04:02 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<Z<a) 
September 11th, 2011, 06:25 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, 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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finding, normal, random, standard, variable 
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