The required probabilities are found using the given graphs of the
probability distributions.
Response:
1) P(X< 5) is D) 0.7
2) The probability equal to 0.2 are;
- P(X ≤ 2)
- P(X ≥ 4)
How can the probabilities be calculated from the graph of a probability distribution?
The probabilities are given by the area under the curve of the graph of
the probability distribution, which are found as follows;
1) The given figure is a trapezium, which gives;
[tex]Area \ of \ a \ trapezium = \mathbf{\dfrac{a + b}{2} \cdot h}[/tex]
Where;
a, and b are the parallel sides of the trapezium
h = The height
Therefore;
[tex]P(X < 5) = \dfrac{5 + 2}{2} \times 0.2 = \mathbf{0.7}[/tex]
2) The probabilities equal to 0.2 are found as follows;
1) At P(X ≤ 2), the area is a triangle, which gives;
[tex]Area \ of \ a \ triangle = \mathbf{\dfrac{1}{2} \times Base \ length \times Height\sqrt{x}}[/tex]
[tex]P(X \leq 2) = \dfrac{1}{2} \times 2 \times 0.2 = \mathbf{0.2}[/tex]
2) At P(X ≥ 4), has a triangular area, which gives;
[tex]P(X \geq 4) = \mathbf{\dfrac{1}{2} \times 1 \times 0.4}= 0.2[/tex]
3) P(2 ≤ X ≤4) has a trapezoidal area, which gives;
[tex]P( 2 \leq X \leq 5) = \mathbf{\dfrac{0.2 + 0.4}{2}} \times 0.2 = 0.6[/tex]
P(2 ≤ X ≤4) = 0.6 ≠ 0.2
4) P(1 ≤ X ≤ 3) has a trapezoidal area, which gives;
[tex]P( 1 \leq X \leq 3) = \dfrac{0.1 + 0.3}{2} \times 2 = 0.4[/tex]
P(1 ≤ X ≤ 3) = 0.4 ≠ 0.2
Therefore;
The probabilities that are equal to 0.2 are;
- P(X ≤ 2) = 0.2
- P(X ≥ 4) = 0.2
Learn more about probability distributions here:
https://brainly.com/question/11290242
