Answer:
a = 5.
Step-by-step explanation:
The graph here is a probability density graph. What will represent [tex]P(X\le a)[/tex] on the graph?
[tex]P(X\le a)[/tex] is the area
- between the graph and the x-axis,
- to the left of [tex]a[/tex].
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 [tex]\displaystyle \frac{1}{2}\times 0.2\times 4 = 0.4[/tex],
- A rectangle of area [tex]0.2 \times (5 - 4) = 0.2[/tex], and
- Another right triangle of area [tex]\displaystyle \frac{1}{2} \times 0.2 \times (9 - 5) = 0.4[/tex].
The area of the leftmost triangle plus that of the rectangle is exactly 0.6. In other words, the area to the left of [tex]a = 5[/tex] between the graph and the x-axis is [tex]0.6[/tex]. [tex]P(X \le 5) = 0.6[/tex]. [tex]a = 5[/tex].
As a side note [tex]a = 5[/tex] shall be the only answer to this question since the area under the graph to the left of [tex]a[/tex] can only increase or stay constant but not decrease as the value of [tex]a[/tex] increases.
