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Chapter 6: Q. 6.88 (page 276)

State the empirical rule as specialized to variables.

Short Answer

Expert verified

The percentage that is within one standard deviation of the mean is roughly 68.26%.

The percentage within two standard deviations of the mean is 95.44per cent.

Around 99.74per cent are within three standard deviations of the mean.

Step by step solution

01

Concept introduction

The quantity of one variable in algebraic equations is typically reliant on the position of another. If the data tuple isn't declared precisely, the variable's beginning value reflects the default value.

02

Explanation

Normal distributions have a bell shape to them. As a result, the empirical rule is as follows:

For the distributed variable with a bell shape,

- The percentage of observations that are within one standard deviation of the mean is roughly 68.26%.

- The percentage of observations that are within two standard deviations of the mean is 95.44%.

- Around of observations are within three standard deviations of the mean.

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Most popular questions from this chapter

A variable is normally distributed with a mean 10 and standard deviation3. Find the percentage of all possible values of the variable that

a. lie between 6and 7.

b. are at least 10 .

c. are at most 17.5 .

DetermineZ0.015

11. Answer true or false to each statement. Explain your answers.

a. Two normal distributions that have the same mean are centered at the same place, regardless of the relationship between their standard deviations.

b. Two normal distributions that have the same standard deviation have the same spread, regardless of the relationship between their means.

The area under a density curve that lies to the left of 60 is 0.364. What percentage of all possible observations of the variable are

a. Less than 60?

b. At least 60?

Each year, thousands of high school students bound for college take the Scholastic Assessment Test (SAT). This test measures the verbal and mathematical abilities of prospective college students. Student scores are reported on a scale that ranges from a low of 200to a high of 800. Summary results for the scores are published by the College Entrance Examination Board in College Bound Seniors. In one high school graduating class, the SAT scores are as provided on the WeissStats site. Use the technology of your choice to answer the following questions.

a. Do the SAT verbal scores for this class appear to be approximately normally distributed? Explain your answer.

b. Do the SAT math scores for this class appear to be approximately normally distributed? Explain your answer.
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