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Chapter 6: Q. 6.81 (page 269)

Determine the two z-scores that divide the area under the standard normal curve into a middle 0.90 area and two outside 0.05areas.

Short Answer

Expert verified

The z-score under the typical normal curve with area 0.05to the left is around -1.645. The z-score with the area 0.05to its right under the typical normal curve will be1.645.

Step by step solution

01

Given information

The given areas

Middle area is 0.90

Two outside areas are0.05.

02

Explanation

The given middle area is 0.90

Two outside areas are 0.05.

Begin by looking for the area 0.05in the table's body. It is not in the table, and the closest values are 0.0495and 0.0505in the table. -1.645is the average of two z-scores of -1.64and -1.65.

As a result, the z-score under the typical normal curve with area 0.05to the left is around -1.645. The z-score with the area 0.05to its right under the typical normal curve will be 1.645using the symmetry property, which can be depicted as

Below is a section of the standard normal table that is relevant:

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Most popular questions from this chapter

According to Table II, the area under the standard normal curve that lies to the left of 1.05is 0.8531. Without further reference to Table II, determine the area under the standard normal curve that lies

a. to the right of 1.05.

b. to the left of -1.05.

c. between -1.05and1.05

Female College Students. Refer to Example 6.3 on page 256 .

a. Use the relative-frequency distribution in Table 6.1 to obtain the percentage of female students who are between 60and65inches tall.

b. Use your answer from part (a) to estimate the area under the normal curve having parameters 渭=64.4and蟽=2.4that lies between 60and65. Why do you get only an estimate of the true area?

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The area under a density curve that lies between 5 and 6 is 0.728. What percentage of all possible observations of the variable are cither less than 5 or greater than 6 ?

15. Explain how to use Table II to determine the z-score that has a specified area to its

a. left under the standard normal curve.

b. right under the standard normal curve.
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