Question

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

Use the probability distribution graph to answer the question.

P(X ≤ a) = 0.6

What is the value of a?

Answer 1

a = 5.

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 (1)/(2)* 0.2* 4 = 0.4`,
• A rectangle of area
  `0.2 * (5 - 4) = 0.2`, and
• Another right triangle of area
  `\displaystyle (1)/(2) * 0.2 * (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.