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Chapter 6: Q. 17 (page 287)

State the empirical rule for variables.

Short Answer

Expert verified

The empirical rule for variables:

About 99.7%of all possible observations lie here.

About 95%of all possible observations lie here.

About68%of all possible observations lie here.

Step by step solution

01

Concept Introduction

Empirical rule is useful because it indicates the intervals or numbers which indicates the percent area lies between them. It is useful because it give us idea about the percentage of the data between the two points approximately.

02

Explanation

A proper empirical rule indicates that approximately 68.5%of values lie in the interval.

A proper empirical rule indicates that approximately 95.5%of values lie in the interval.

By a proper empirical rule, approximately 99.7%of values are in the interval.

The curve is as follows:

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Most popular questions from this chapter

We have provided a normal probability plot of data from a sample of a population. In each case, assess the normality of the variable under consideration.

Obtain the z-score that has an area0.70 to its right.

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.

Briefly, for a normally distributed variable, how do you obtain the percentage of all possible observations that lie within a specified range?
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