( SHOW ALL WORK) Here we find a z-score that corresponds to a given percentile (

Question

( SHOW ALL WORK)

Here we find a z-score that corresponds to a given percentile

(a) Find the z-score that marks the 85th percentile (denoted P85). That is, find the z-score that delineates the lower 85% from the upper 15% of all the z-scores.

(b) Find the z-score that marks the 25th percentile (denoted P25). That is, find the z-score that

delineates the lower 25% from the upper 75% of all the z-scores.

Here we find the z-scores that delineate the middle portions of the standard normal distribution.

(a) Find the range of z-scores that constitute the middle 95% of all values from the others.

(b) Find the range of z-scores that constitute the middle 99% of all values from the others.

Explanation / Answer

a)

P( z < z) = 0.85 that is the same that say P( z > z) = 0.15

using table

z = 1.03

b)

P( z < z) = 0.25

z = - 0.67

c)

P( z<z) = 0.025 and P( z > z ) = 0.025

Z = +/- 1.96

d)

P(z < z) = 0.005 and P( z > z ) = 0.005

Z = +/- 2.57

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