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I am having a bit of trouble with this question here

P {-2 < Z < -1} = P { 1 < Z < x}

The question asks to find the value of X when Z is a standard normal random variable.

How would one approach this question? Do you solve the Z score for the first part first ?

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    $\begingroup$ The best approach is to sketch the density function of the standard normal, and then to use symmetry. The probability that $-2\le Z\le -1$ is the area of a certain region. You could first compute $\Pr(-2\le Z\le -1)$ first, but that is definitely not the best strategy for this problem. $\endgroup$ – André Nicolas Sep 14 '15 at 16:36
  • $\begingroup$ Im still a bit confused, I can easy sketch the graph here and find probability -2 < Z < -1 but im still frustrated on how I would find x. $\endgroup$ – reed20 Sep 14 '15 at 17:02
  • $\begingroup$ The density function of the standard normal (the usual bell-shaped curve) is symmetric about the $y$-axis. So $\Pr(-2\le Z\le -1)=\Pr(1\le Z\le 2)$. $\endgroup$ – André Nicolas Sep 14 '15 at 17:06
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Write it in terms of the standard Normal distribution.Use $\Phi(x)=1-\Phi(-x)$.

Hence $$P(-2 < Z < -1)=\Phi(-1)-\Phi(-2)=\Phi(2)-\Phi(1).$$ Hence, $x=2$.

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