The area under the graph of the continuous uniform distribution is 1.
a. The probability that the value will be between 5 and 7 is the area between 5 and 7.
[tex]P(5 \ \textless \ x \ \textless \ 7) = \frac{2}{10} = \frac{1}{5}[/tex]
b. The probability that the value will be between 2 and 3 is the are between 2 and 3.
[tex]P(2 \ \textless \ x \ \textless \ 3)=\frac{1}{10}[/tex]
c. The mean is given by:
[tex]\mu=\frac{a+b}{2}=\frac{0+10}{2}=5[/tex]
d. The variance is given by:
[tex]\sigma^2}=\frac{1}{12}(b-a)^{2}=\frac{1}{12}(10)^{2}=8.3333[/tex]
The standard deviation is:
[tex] \sqrt{\sigma} = \sqrt{8.3333} =2.887[/tex]
