Find the z-values corresponding to the following areas:
Find z such that 6% of the standard normal curve lies to the left of z.
Find z such that 55% of the standard normal curve lies to the left of z.
Find z such that 8% of the standard normal curve lies to the right of z.
Find z such that 82% of the standard normal curve lies to the right of z.
Find z such that 80% of the standard normal curve lies between –z and z.
solution:
Using standard normal table,
P(Z < z) = 6%
=(Z < z) = 0.06
= P(Z < z ) = 0.06
z=-1.56
2.
Using standard normal table,
P(Z < z) = 55%
=(Z < z) = 0.55
= P(Z < z ) = 0.55
z=0.13
3.
Using standard normal table,
P(Z > z) = 8%
= 1 - P(Z < z) = 0.08
= P(Z < z) = 1 - 0.08
= P(Z < z ) = 0.92
z =1.41
4.
Using standard normal table,
P(Z > z) = 82%
= 1 - P(Z < z) = 0.82
= P(Z < z) = 1 - 0.82
= P(Z < z ) = 0.18
z =-0.92
5.
middle 80% of score is
P(-z < Z < z) = 0.80
P(Z < z) - P(Z < -z) = 0.80
2 P(Z < z) - 1 = 0.80
2 P(Z < z) = 1 + 0.80 = 1.80
P(Z < z) = 1.80 / 2 = 0.90
P(Z <1.28 ) = 0.90
z ± 1.28
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