Problem I Find the probabilities that a random variable hav

Problem # I Find the probabilities that a random variable having the standard normal distribution will take on a value (a) between 0.87 and 1.28; (b) between -0.34 and 0.62; (c) greater than 0.85; (d) greater than -0.65.

Solution

a)

z1 = lower z score =    0.87      
z2 = upper z score =     1.28      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.807849798      
P(z < z2) =    0.899727432      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.091877634   [ANSWER]

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b)

z1 = lower z score =    -0.34      
z2 = upper z score =     0.62      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.366928264      
P(z < z2) =    0.732371107      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.365442843   [ANSWER]  

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c)

Using a table/technology, the right tailed area of this is          
          
P(z >   0.85   ) =    0.197662543 [ANSWER]

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d)

Using a table/technology, the right tailed area of this is          
          
P(z >   -0.65   ) =    0.742153889 [ANSWER]