Answer
a. $\frac{6}{5}$;
b. $-\frac{31}{20}$
c. $\frac{27}{50}$
Work Step by Step
We are given $f(x)=\frac{1}{10}$
for x in $[10,20]$
a. $P(X\leq12)=\lim\limits_{a \to -\infty}\int^{12}_{a}\frac{1}{10}dx=\lim\limits_{a \to -\infty}(\frac{1}{10}x)|^{12}_{a}=\lim\limits_{a \to -\infty}(\frac{6}{5}-\frac{1}{10}a)=\frac{27}{50}$
b. $P(X\geq\frac{31}{2})=\lim\limits_{b \to \infty}\int^{b}_{\frac{31}{2}}\frac{1}{10}dx=\lim\limits_{b \to \infty}(\frac{1}{10}x)|^{b}_{\frac{31}{2}}=\lim\limits_{b \to \infty}(\frac{1}{10}b-\frac{31}{20})=-\frac{31}{20}$
c. $P(10.8 \leq X \leq 16.2)=\int^{16.2}_{10.8}\frac{1}{10}dx=\frac{1}{10}x|^{16.2}_{10.8}=\frac{1}{10}$
