The pdf of this law is given by the formula :
[tex]\dfrac{1}{190-110}\text{ if } 110\leq x\leq190 \text{ and 0 otherwise.}[/tex]
We will use the above formula in order to compute the probability like this:
[tex]\dfrac{1}{80}\int_{95}^{165}dx=\dfrac{1}{80}\int_{110}^{165}dx\\
=\dfrac{1}{80}(165-110)\\=\dfrac{55}{80}[/tex]
Similarly, we find the second probability (question 2) like this:
[tex] \frac{190-120}{80}= \frac{70}{80}=\frac{7}{8}[/tex].
The variance is given by the formula:
[tex] \frac{1}{12}80^2 =\frac{800}{12} [/tex]
