Chapter 2: Q. 8 (page 137)

R2.8 Working backward
(a) Find the number $z$ at the 80th percentile of a standard Normal distribution.
(b) Find the number localid="1649404103275" $z$ such that localid="1649404108890" $35 %$ of all observations from a standard Normal distribution are greater than localid="1649404115271" $z$ .
- Use Table A to find the percentile of a value from any Normal distribution and the value that corresponds to a given percentile.

Expert verified

a. The number $z$ at the 80th percentile of a standard Normal distribution is $0.84$

b. The number $z$ such that $35 %$ of all observations from a standard Normal distribution are greater than $z$ is $0.39$

Step by step solution

Standard Normal distribution Percentile $= 80 t h$ percentile

Value of $z = ?$

Table A shows the probabilities of values smaller than a $z -$ score.

The $80$ th percentile probability is $80 %$ or $0.80$ for a value less than the $80$ th percentile.

Table A provides the z-score, which corresponds to $0.80$ probability.

$z = 0.84$

Standard Normal distribution Percentile $= 35 %$

Value of $z = ?$

Probabilities of values smaller than a z-score can be found in Table A.

The reason is that $35 %$ of all observations are bigger than z and thus $65 %$ or $0.65$ of all observations are smaller than z.

Table A shows a z-score of $0.65$ , which is approximately the probability of success

$z = 0.39$

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