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Chapter 6: Q.6.118 (page 283)

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

Short Answer

Expert verified

The data is spread in a linear way.

Step by step solution

01

Given Information

Consider the concept of "variable normalcy."

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

02

Explanation

The normalcy probability plot is a graphical method for determining whether or not data is normally distributed. The line is constructed between observed variable values and normal scores. If the variable is regularly distributed, the plot should be linearly approximated; otherwise, it should not be.

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Most popular questions from this chapter

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.

Explain how Table II is used to determine the area under the standard normal curve that lies

a. to the left of a specified z-score.

b. to the right of a specified z-score.

c. between two specified z-scores.

In each part, find the area under the standard normal curve that lies between the specified z-scores, sketch a standard normal curve and shade the area of interest.

a. -1and 1

b. -2and 2

c. -3and 3

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

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 ?
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