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Chapter 6: Q. 6.86 (page 276)

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

Short Answer

Expert verified

Step 1: The connected variable's normal curve is drawn.

Step 2: The region of interest is shaded, and the x-value(s) noted

Step 3: The z-score(s) are calculated.

Step 4: Using the standard normal table, get the area under the standard normal curve.

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

First, determine the equivalent area under the standard normal curve by expressing the range in terms of z-scores.

The steps are as follows:

Step 1: The connected variable's normal curve is drawn.

Step 2: The region of interest is shaded, and the x-value(s) that define it are noted.

Step 3: Calculate the z-score(s) for the delimiting x-value(s).

Step 4: Using the standard normal table, get the area under the standard normal curve delimited by the z-score(s).

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Most popular questions from this chapter

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.

State the empirical rule as specialized to variables.

Let 0<α<1. Show that for a regularly distributed variable 100(1-α)%of all possible observations lie within zα/2standard deviations to either side of the mean, that is, between μ-zF/2·σand μ+zσ/2·σ.

Determinez0.33

Obtain the following z-scores

a. z0.20

b.z0.06
See all solutions

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