Question

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!

Answer 1

Answer:

a = 5.

Step-by-step explanation:

The graph here is a probability density graph. What will represent $P(X\le a)$ on the graph?

$P(X\le a)$ is the area

• between the graph and the x-axis,
• to the left of $a$.

The area under the graph between 0 and 9 is a trapezoid. Consider the trapezoid in three slices from left to right:

• A right triangle of area $\displaystyle \frac{1}{2}\times 0.2\times 4 = 0.4$,
• A rectangle of area $0.2 \times (5 - 4) = 0.2$, and
• Another right triangle of area $\displaystyle \frac{1}{2} \times 0.2 \times (9 - 5) = 0.4$.

The area of the leftmost triangle plus that of the rectangle is exactly 0.6. In other words, the area to the left of $a = 5$ between the graph and the x-axis is $0.6$. $P(X \le 5) = 0.6$. $a = 5$.

As a side note $a = 5$ shall be the only answer to this question since the area under the graph to the left of $a$ can only increase or stay constant but not decrease as the value of $a$ increases.