Question

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

Short answer

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

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.

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).