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Chapter 6: Q6.7 (page 260)

The area under the density curve that lies to the right of 15 is 0.324. What percentage of all possible observations of the variable

a. exceed 15 ?

b. are at most 15 ?

Short Answer

Expert verified

Percentage of variable's observations that exceed 15=32.4%

Percentage of variable's observations that are at most15=67.6%

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 =45.3Kgs

02

Density Curve Probability

It shows likelihood ( probability) of continuous variable' outcomes. As total probability = 1, total area under the curve is also equal to1

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 under the density curve that lies to the right of 15=0.324out of total area = 1, so percentage of observations more than 15=32.4%

Hence, percentage of observations that are at most 15include observations that are less than or equal to 15. These observations are to the left of 15, so 1-0.324=67.6%

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