Given a standard normal distribution determine the following

Given a standard normal distribution, determine the following. Show Table Values used in each part. P(Z 1.4) P(Z

Solution

A)

Using a table/technology, the left tailed area of this is          
          
P(z <   1.4   ) =    0.9192 [ANSWER]

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b)

P(z>1.4) = 1 - P(z<1.4) = 1-0.9192 = 0.0808 [ANSWER]

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c)

P(z<-1.4) = P(z>1.4)

by symmetry. Thus,

p(z<-1.4) = 0.0808 [ANSWER]

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d)

z1 = lower z score =    -0.5      
z2 = upper z score =     1      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.3085      
P(z < z2) =    0.8413      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.5328 [ANSWER]

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e)

z1 = lower z score =    0.5      
z2 = upper z score =     1.5      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.6915      
P(z < z2) =    0.9332
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.2417 [ANSWER]