Answer:
a) Mean = 1205
Standard Deviation = 2.89
b) P( 1195 < x < 1205) = 0.5
50% of the cables lie within the given specification.
Step-by-step explanation:
We are given the following information in the question:
[tex]f(x) = 0.1[/tex]
a = 1200, b = 1210
We are given a uniform distribution.
a) Mean:
[tex]\mu = \displaystyle\frac{a+b}{2}\\\\\mu = \frac{1200+1210}{2} = 1205[/tex]
Standard Deviation:
[tex]\sigma = \sqrt{\displaystyle\frac{(b-a)^2}{12}}\\\\= \sqrt{\displaystyle\frac{(1210-1200)^2}{12}} = \sqrt{8.33} = 2.89[/tex]
b) P( 1195 < x < 1205)
[tex]=\displaystyle\int_{1195}^{1205} f(x) dx\\\\=\displaystyle\int_{1200}^{1205} (0.1) dx\\\\=0.1[x]_{1200}^{1205} = (0.1)(1205-1200) = 0.5[/tex]
50% of the cables lie within the given specification.
