Let Z be a standard normal random variable and calculate the

Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wherever appropriate. (Round your answers to four decimal places.)

Solution

a)

z1 = lower z score =    0      
z2 = upper z score =     2.17      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.5      
P(z < z2) =    0.984996577      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.484996577   [ANSWER]

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b)

z1 = lower z score =    0      
z2 = upper z score =     2      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.5      
P(z < z2) =    0.977249868      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.477249868   [ANSWER]

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c)

z1 = lower z score =    -2.3      
z2 = upper z score =     0      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.01072411      
P(z < z2) =    0.5      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.48927589   [ANSWER]

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d)

z1 = lower z score =    -2.3      
z2 = upper z score =     2.3      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.01072411      
P(z < z2) =    0.98927589      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.97855178   [answer]  
  
  

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