Question

Assume a normal distribution. (Give your answer correct to two decimal places.)

(a) Find the z-score associated with the 59th percentile.

(b) Find the z-score associated with the 82nd percentile.

(c) Find the z-score associated with the 92nd percentile.

Answer 1

Answer:

Given that,

Assume a normal distribution.

(a).

Find the z-score associated with the 59th percentile:

P(Z < z)=59%

P(Z < z)=0.59

[Since from normal distribution table]

P(Z < 0.23)=0.59

z=0.23

(b).

Find the z-score associated with the 82nd percentile:

P(Z < z)=82%

P(Z < z)=0.82

[Since from normal distribution table]

P(Z < 0.92)=0.82

z=0.92

(c).

Find the z-score associated with the 92nd percentile:

P(Z < z)=92%

P(Z < z)=0.92

[Since from normal distribution table]

P(Z < 1.41)=0.92

z=1.41