Question

A uniform density curve goes from negative 5 to positive 1.

Answer 1

Answer: Choice B) One-sixth

In other words, the fraction 1/6

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Explanation:

The base, aka horizontal component, is 6 units long. Count out the spaces from -5 to 1 to get a result of 6.

Or you could subtract and use absolute value in either of these two ways

• |A - B| = |-5 - 1| = |-6| = 6
• |B - A| = |1 - (-5)| = |1 + 5| = |6| = 6

Where A = -5 and B = 1 are the endpoints mentioned. Absolute value is used to ensure the result of the subtraction isn't negative. Negative distance on a number line doesn't make sense.

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However you determine the base, we'll multiply it by the unknown height which we'll call h. This leads to the area of the rectangle. The area is 6h.

Rule: The area under a probability density curve must always be 1.

So the area 6h must be 1 which helps us see that...

6h = 1

h = 1/6

Divide both sides by 6 to isolate h fully.