(b) Compute Pp:

(b) Compute P(x < 45). When dealing with continuous distributions, the probability will be for a range of values instead of a single value. This probability will be the area under the graph between the given values. For a = 40 and b = 50, the height of the density function was found to be 0.10. This gives the following uniform probability density distribution. f(x) = 1 o 0.10 o elsewhere 40 x s 50 elsewhere The graph of this distribution is a rectangle, which has an area equal to the width multiplied by the height. The height was found to be 0.10, so the width is needed. Since the desired probability is that x < 45, and this distribution is only valid when x is between 40 and 50, the rectangle representing this probability will be between 40 and45 C , giving a width of X . Find the area of this rectangle, which is also P(x < 45). P(x < 45) = width height