X U 2 0 Find Xc so that ProbX Xc 025 NOTE write your answe

X ~ U [-2, 0] Find Xc so that Prob(X >Xc) = 0.25 NOTE write your answer using 4 decimal digits. DO NOT ROUND UP OR DOWN. Consider the random variable Z ~ N(0, 1). Find Prob(-0.6

Solution

1.

here,

P(X>Xc) = P(Xc<X<0)

Thus,

P(X>Xc) = (0 - Xc) / (0-(-2)) = 0.25

-Xc/2 = 0.25

Xc = -0.5 [ANSWER]

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2)

z1 = lower z score =    -0.6      
z2 = upper z score =     -0.3      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.274253118      
P(z < z2) =    0.382088578      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.10783546   [ANSWER]