Question

# Find the z-values corresponding to the following areas: Find z such that 6% of the standard...

Find the z-values corresponding to the following areas:

1. Find z such that 6% of the standard normal curve lies to the left of z.

2. Find z such that 55% of the standard normal curve lies to the left of z.

3. Find z such that 8% of the standard normal curve lies to the right of z.

4. Find z such that 82% of the standard normal curve lies to the right of z.

5. 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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