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Chapter 6: Q. 6.84 (page 269)

In this section, we mentioned that the total area under any curve representing the distribution of a variable equals . Explain why.

Short Answer

Expert verified

The total probability of a variable equals one is a well-known fact.

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

The overall area under the curve can be interpreted as the variable's total probability.

The total probability of a variable equals one is a well-known fact.

As a result, the entire area under any curve reflecting a variable's distribution is equal to1.

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Most popular questions from this chapter

Obtain the z-score that has an area of 0.95 to its right.

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.

Answer true or false to each statement. Give reasons for your answers.

a. Two variables that have the same mean and standard deviation have the same distribution.

b. Two normally distributed variables that have the same mean and standard deviation have the some distribution.

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.

DetermineZ0.015
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