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Chapter 6: Q6.9 (page 260)

The area under the density curve that lies between 15and 20is 0.414. What percentage of all possible observations of the variable are either less than 15or greater than 20?

Short Answer

Expert verified

Percentage of the variable's observations less than 15or greater than 20= 58.6%

Step by step solution

01

Density Curve Concept 

Density Curve is a graphical representation of numerical distribution, having variable outcomes that are continuous (which can take non whole values), like weight = 54.3Kgs

02

Density Curve Probability 

It shows likelihood ( probability) of continuous variable' outcomes. As total probability = 1, total area under the curve is also equal to 1.

Percentage of total observations that lie within a range is equal to percentage of area under the curve between the corresponding values.

03

Explanation

As total area = 1& area between values 15& 20= 0.414

So area to the left of 15or to the right of 20= total area - area between the numbers = 1-0.414=0.586

Hence, percentage of observations less than 15or greater than 20=58.6%

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