Given a standardized normal distributionwa mean of 0 and sta

Given a standardized normal distribution(w/a mean of 0 and standard deviation of 1), what is the probability that:

a. Z is <1.57?

b. Z is >1.84?

c. Z is between 1.57 & 1.84?

d. Between what 2 X values (symmetrically distributed around the mean)are 80%of the values?

Solution

a)

Using a table/technology, the left tailed area of this is          
          
P(z >   1.57   ) =    0.941792444 [answer]

b)

Using a table/technology, the right tailed area of this is          
          
P(z >   1.84   ) =    0.032884119 [answer]

c)

z1 = lower z score =    1.57      
z2 = upper z score =     1.84      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.941792444      
P(z < z2) =    0.967115881      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.025323437   [answer]

d)

Getting the outward areas of the two extreme tails,          
          
alpha/2 = (1-middle area)/2 =    0.1      
          
Thus, the z values bounding these tails, using table/technology,          
          
z1 = lower z value =    -1.281551566      
z2 = upper z value =    1.281551566   [ANSWERS]