For a standard normal distribution, determine the probabilities of obtaining the following z values. It is helpful to draw a normal distribution for each case and show the corresponding area.
(a)
greater than zero
(b)
between −2.0 and −1.5
(c)
less than 1.5
(d)
between −1.2 and 1.2
(e)
between 1.35 and 1.85
Solution
Using standard normal table
a ) P ( Z < - 0.64 )
= 0.2611
Probability = 0.2611
b ) P ( Z > 0 )
1 - P ( Z < 0)
= 1 - 0.5000
= 0.5000
Probability = 0.5000
b ) P ( −2.0 < Z < -1.5 )
P ( Z < -1.5 ) - P ( Z < −2.0)
= 0.0668 - 0.0228
= 0.0440
Probability = 0.0440
c ) P ( Z < 1.5 )
= 0.9332
Probability = 0.9332
d ) P ( −1.2 < Z < 1.2 )
P ( Z < 1.2 ) - P ( Z < −1.2 )
= 0.8849 - 0.1151
= 0.7698
Probability = 0.7698
e ) P ( 1.35 < Z < 1.85 )
P ( Z < 1.85 ) - P ( Z < 1.35 )
= 0.9678 - 0.9115
= 0.0563
Probability = 0.0563
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