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Chapter 2: Q. 8 (page 137)

R2.8 Working backward

(a) Find the number zat the 80th percentile of a standard Normal distribution.

(b) Find the number localid="1649404103275" zsuch 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.

Short Answer

Expert verified

a. The number zat the 80th percentile of a standard Normal distribution is 0.84

b. The numberzsuch that 35%of all observations from a standard Normal distribution are greater thanzis0.39

Step by step solution

01

Part(a) Step 1: Given Information

Standard Normal distribution Percentile=80thpercentile

Value ofz=?

02

Part(a) Step 2: Explanation

Table A shows the probabilities of values smaller than az-score.

The 80th percentile probability is 80%or 0.80for a value less than the80th percentile.

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

z=0.84

03

Part(b) Step 1: Given Information

Standard Normal distribution Percentile =35%

Value ofz=?

04

Part(b) Step 2: Explanation

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 0.65of 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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