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Chapter 6: Q6.8 (page 260)

The area under the density curve that lies between 30and 40is 0.832. What percentage of all possible observations of the variable are either less than 30or greater than 40?

Short Answer

Expert verified

Percentage of variable's observations that are less than 30 or greater than 40 =16.8%

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 =45.3kg

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 30&40=0.832

So area to the left of 30or to the right of 40= total area - area between the numbers = 1-0.832=0.168

Hence, percentage of observations less than 30or greater than 40= 16.8%

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