Given that z is a standard normal random variable, find z for each situation. (Round your answers to two decimal places.)
(a) The area to the right of z is 0.01
(b) The area to the right of z is 0.025.
(c) The area to the right of z is 0.05
(d) The area to the right of z is 0.10
Solution :
Given that,
Using standard normal table ,
(a)
P(Z > z) = 0.01
1 - P(Z < z) = 0.01
P(Z < z) = 1 - 0.01
P(Z < 2.33) = 0.99
z = 2.33
(b)
P(Z > z) = 0.025
1 - P(Z < z) = 0.025
P(Z < z) = 1 - 0.025
P(Z < 1.96) = 0.975
z = 1.96
(c)
P(Z > z) = 0.05
1 - P(Z < z) = 0.05
P(Z < z) = 1 - 0.05
P(Z < 1.65) = 0.95
z = 1.65
(d)
P(Z > z) = 0.10
1 - P(Z < z) = 0.10
P(Z < z) = 1 - 0.10
P(Z < 1.28) = 0.9
z = 1.28
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