Please show and explain your work THANK YOU Find the follow

Please show and explain your work. THANK YOU !!

Find the following probabiliteis for the normal curve:

Solution

a)

Using a table/technology, the left tailed area of this is          
          
P(z <   1.23   ) =    0.890651448 [ANSWER]

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b)

z1 = lower z score =    -1      
z2 = upper z score =     2      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.158655254      
P(z < z2) =    0.977249868      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.818594614   [ANSWER]

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c)

Using a table/technology, the left tailed area of this is          
          
P(z <   0   ) =    0.5 [ANSWER]

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d)

z1 = lower z score =    -0.57      
z2 = upper z score =     1.57      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.284338849      
P(z < z2) =    0.941792444      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.657453595   [ANSWER]