Question

Suppose the sample space for a continuous random variable is 0 to 8. If the area under the density curve for the variable from 0 to 5 is 0.625, what is the area under the density curve from 5 to 8?

Answer 1

Answer: 0.375

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Step-by-step explanation:

The portion from x = 0 to x = 5 has area 0.625, so 62.5% of the total area is accounted for. The remaining 100% - 62.5% = 37.5% of the total area must be in the remaining portion from x = 5 to x = 8. Convert 37.5% to decimal form to get the answer 0.375

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Another approach

We have two disjoint areas under a curve. The two areas must add to 1. Let A be the unknown area

So,

0.625+A = 1

A = 1-0.625

A = 0.375

The area under the curve from x = 5 to x = 8 is 0.375