Answer:
a) 0.2
b) 0.4
c) Mean = 62.5
Variance = 52.083
Step-by-step explanation:
We are given the following information in the question:
[tex]f(x) = 0.4\\[/tex]
a = 50, b = 75
We are given a uniform distribution.
a) P(x > 70)
[tex]P(x > 70)\\=1 - P( \leq 70)\\\\=1-\displaystyle\int^{70}_{50}0.04 ~dx\\\\=1-0.04(70-50)\\=0.2[/tex]
b) P(x < 60)
[tex]P(x < 60)\\\\=\displaystyle\int^{60}_{50}0.04 ~dx\\\\=0.04(60-50)\\=0.4[/tex]
c) Mean:
[tex]\mu = \displaystyle\frac{a+b}{2}\\\\\mu = \frac{50+75}{2} = 62.5[/tex]
Variance:
[tex]\sigma^2 = \displaystyle\frac{(b-a)^2}{12}\\\\= \displaystyle\frac{(75-50)^2}{12} = 52.083[/tex]
