Elementary Statistics: A Step By Step Approach - 9 Edition - Chapter 6.1 - Problem 49e
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# Find two z values, one positive and one negative, that are

Elementary Statistics: A Step By Step Approach | 9th Edition

Problem 49E

Find two z values, one positive and one negative, that are equidistant from the mean so that the areas in the two tails total the following values.

a. 5%

b. 10%

c. 1%

Accepted Solution
Step-by-Step Solution:

Step 1 of 3

Our goal is:

We need to find two z-values.

a). Given 5%.

From the given information we know that P(-z<Z or Z>z) = 5% = 0.05.

Then the table (area under the normal curve) the probability of values smaller than a certain z-score of the standard normal distribution.

Now the standard normal distribution is symmetric about 0.     0.025

Here we have to determine the corresponding z-score in area under the normal curve table.

The corresponding z-score z is then given in row/column title of area under the normal curve table which corresponding to a probability of 0.025 or the probability closest.

-z = -1.96

Hence, the two z-score is z = 1.96 (z = +1.96 or z = -1.96).

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###### Chapter 6.1, Problem 49E is Solved

Step 2 of 3

Step 3 of 3

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