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Chapter 6: Problem 55

Determine the value of \(z\) so that the area under the standard normal curve a. in the right tail is \(.0500\) b. in the left tail is \(.0250\) c. in the left tail is \(.0100\) d. in the right tail is \(.0050\)

Short Answer

Expert verified
The respective z-values for the areas under standard normal curve are: a. 1.645 b. -1.960 c. -2.326 d. 2.576

Step by step solution

01

Find Z-values for each part

Use a normal distribution table or a calculator that can find z-values for given areas under the curve. The procedure slightly differs depending on whether the area is in the left or right tail.
02

Determine z for right tail area = .0500

To determine z for a given area in the right tail, just use the calculator or table directly. The area (.0500) corresponds to a z score of about 1.645.
03

Determine z for left tail area = .0250

Be mindful that the measures in the table or calculator are for the area between center (z=0) and the z value we are looking for. Therefore, if the area is given for left tail, one should subtract it from .5000 (because total area on the left of center is .5000 in standard normal distribution). So, for left tail area .0250, look up .5000 - .0250 = .4750 on the table or calculator to get the z-value. That gives a z value about -1.960.
04

Determine z for left tail area = .0100

Apply similar logic as in step 2 for the left tail area .0100. Look up .5000 - .0100 = .4900. The corresponding z value is about -2.326.
05

Determine z for right tail area = .0050

For the right tail area .0050, we can directly find the z-value as similar to step 1. The corresponding z value is about 2.576.

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