Suppose x is a continuous random variable with the pdf fx x2

Suppose x is a continuous random variable with the pdf f(x)= x/2 ,0 le X le 2 Find: F(x) = P [X le x| Compute: P(0.5 le X le 1.5) If X is normally distributed with mu = 80 and sigma =10 find the following P[X le 100] P[X ge 70]

Solution

b)

i.

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    100      
u = mean =    80      
          
s = standard deviation =    10      
          
Thus,          
          
z = (x - u) / s =    2      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   2   ) =    0.977249868 [ANSWER]

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ii.

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    70      
u = mean =    80      
          
s = standard deviation =    10      
          
Thus,          
          
z = (x - u) / s =    -1      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   -1   ) =    0.841344746 [ANSWER]

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iii.

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.975      
          
Then, using table or technology,          
          
z =    1.959963985      
          
As x = u + z * s,          
          
where          
          
u = mean =    80      
z = the critical z score =    1.959963985      
s = standard deviation =    10      
          
Then          
          
x = critical value =    99.59963985   [ANSWER]  

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