Exercise 4. (10 points) Consider the random variable X N (u, o) with u = 5 and o = 10). (1) Calculate Pr(X &lt; 0). (Note that Pr(Z &lt; -0.5) =...
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Exercise 4. (10 points) Consider the random variable X N (u, o) with
u = 5 and o = 10).
(1) Calculate Pr(X &lt; 0). (Note that Pr(Z &lt; -0.5) = 0.3085, where
Z N(0, 1) ).
(2) Find x such that Pr(X &lt; x) = 0.0250. (Note that Pr(Z &lt; -1.96)
=
0.025, where Z N(0, 1).
Hint: Let Z = =4. Then Z N(0, 1). If X &lt; x then Z = (X - /)/o &lt;
(x - H) /O.

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