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Chapter 6: Q. 6 (page 285)

State two of the main reasons for studying the normal distribution.

Short Answer

Expert verified

The normal distribution can be expressed with a bell-shaped curve.

The curve is as follows:

Step by step solution

01

Given Information

What the two of the main reasons for studying the normal distribution.

02

Explanation

The following are two of the most important reasons to learn the normal distribution.

The result of statistical information relating to practical phenomena can be simply interpreted using the normal distribution.

For example, blood pressure, school grades, and so on.

The normal distribution can be expressed with a bell-shaped curve.

The curve is as follows:

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Most popular questions from this chapter

13. What key fact permits you to determine percentages for a normally distributed variable by first converting to $z -$ scores and then determining the corresponding area under the standard normal curve?

Use Table to obtain the areas under the standard normal curve. Sketch a standard normal curve and shade the area of interest in each problem.

Find the area under the standard normal curve that lies to the right of

a. $2.02$ .

b. $- 0.56$ .

c. $- 4$ .

28. Verbal GRE Scores. The Graduate Record Examination (GRE) is a standardized test that students usually take before entering graduate school. According to the document GRE Guide to the Use of Scores, a publication of the Educational Testing Service, the scores on the verbal portion of the GRE have mean $150$ points and standard deviation $8.75$ points. Assuming that these scores are (approximately) normally distributed,

a. obtain and interpret the quartiles.

b. find and interpret the 99th percentile.

12. Consider the normal curves that have the parameters $μ = 1.5$ and $σ = 3; μ = 1.5$ and $σ = 6.2; μ = - 2.7$ and $σ = 3; μ = 0$ and $σ = 1 .$

a. Which curve has the largest spread?

b. Which curves are centered at the same place?

c. Which curves have the same spread?

d. Which curve is centered farthest to the left?

e. Which curve is the standard normal curve? $σ$

The total area under the following standard normal curve is divided into eight regions.

a. Determine the area of each region.

b. Complete the following table.

See all solutions

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