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Chapter 6: Q.6.117 (page 283)

Explain why assessing the normality of a variable is often important.

Short Answer

Expert verified

The variable's normalcy is significant.

A random variable's normality is a quality of a normal distribution-distributed random variable.

Step by step solution

01

Given Information

Consider the concept of "variable normalcy."

02

Explanation

Many variables are normally distributed or nearly normally distributed in most cases.

These contain both measurement and non-measurement factors.

It is relatively simple to apply statistics while working with the normalcy of the variable.

We'll use this to figure out what kind of statistical test we can use in inferential statistics.

Only normal or approximate normal distributions pass the statistical test.

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Most popular questions from this chapter

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

a. The area under the normal curve with parameters μ=64.4andσ=2.4that lies to the left of 61is0.0783. Use this information to estimate the percentage of female students who are shorter than 61inches.

b. Use the relative-frequency distribution in Table 6.1 to obtain the actual percentage of female students who are shorter than 61 inches.

c. Compare your answers from parts (a) and (b).

Explain in detail what a normal probability plot is and how it is used to assess the normality of a variable.

A variable is normally distributed with mean 6and standard deviation 2.

Part (a): Determine and interpret the quartiles of the variable.

Part (b) Obtain and interpret the 85thpercentile.

Part (c) Find the value that 65%of all possible values of the variable exceed.

Part (d) Find the two values that divide the area under the corresponding normal curve into a middle area of 0.95and two outside areas of 0.025. Interpret your answer.

College-Math Success. Researchers S. Lesik and M. Mitchell explore the difficulty of predicting success in college-level mathematics in the article "The Investigation of Multiple Paths to Success in College-Level Mathematics" (fraternal of Applied Reacuwh in Hreher Eiturarion, Vol. 5. Issue 1. pP, 48-57). One of the variables explored as an indicator of success was the length of time since a college freshman has taken a mathematics course. The article reports that the mean length of time is 0.18 years with a standard deviation of 0.624 years. For college freshmen, let x represent the time, in years, since taking a math course.

A . What percentage of times are at least 0 years?

b. Assuming that x is approximately normally distributed, tose normal curve areas to determine the approximate percentage of times that are at least 0 years.

c. Based on your results from parts (a) and (b), do you think that the length of time since taking a math course for college freshmen is approximately a normally distributed variable? Explain your answer.

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