a Find the probability that the z score from the standard n

(a) Find the probability that the z - score from the standard normal distribution will lie in the following intervals: (i) z s0.5 i 0

Solution

i)

Using a table/technology, the left tailed area of this is          
          
P(z <   0.5   ) =    0.691462461 [ANSWER]

****************

ii)

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]

******************

iii)

z1 = lower z score =    -1      
z2 = upper z score =     1      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.158655254      
P(z < z2) =    0.841344746      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.682689492   [answer]

***********************

iv)

Using a table/technology, the right tailed area of this is          
          
P(z >   1.5   ) =    0.066807201 [answer]