A line starts at (negative 2, 0), goes to (5, question mark), and then goes down to (6, 0). What would the height need to be for this curve to be a density curve? One-fourth One-half StartFraction 1 Over 8 EndFraction StartFraction 1 Over 16 EndFraction
ANSWER
One-half
A density curve is a continuous curve that describes the probability distribution of a continuous random variable. In order to be a density curve, the curve must meet several conditions:
The curve must be non-negative everywhere, meaning it must have a y-value of at least 0 at every point.
The curve must have a total area of 1 under it.
The curve must be symmetrical around the mean of the distribution.
In this case, the curve starts at (negative 2, 0) and goes to (5, question mark). It then goes down to (6, 0). For the curve to be a density curve, the y-value at x=5 must be at least half the distance from the x-axis to the top of the curve. This is because the curve must have a total area of 1 under it, and the area under the curve between x=-2 and x=6 must be 1. Since the curve starts at y=0 and ends at y=0, the curve must reach its maximum height at x=5. Therefore, the height at x=5 must be at least one-half in order for the curve to be a density curve.
