Given : The interval for a uniform distribution : (4, 28)
The density function for the uniform distribution will be :-
[tex]f(x)=\dfrac{1}{28-4}=\dfrac{1}{24}[/tex]
(a) Required interval : (11,24) = [tex]24-11=13[/tex]
Now, the probability that x lies between 11 and 24 is given by :-
[tex]=\text{(Required interval)} \cdot\ f(x)=\dfrac{13}{24}[/tex]
(b) Required interval : (9,22) = [tex]22-9=13[/tex]
Now, the probability that x lies between 9 and 22 is given by :-
[tex]=\dfrac{13}{24}[/tex]
(c) Required interval : (7,19) = [tex]19-7=12[/tex]
Now, the probability that x lies between 9 and 22 is given by :-
[tex]=\dfrac{12}{24}=0.5[/tex]
(d)Required interval : (10,23) = [tex]23-10[/tex]
Now, the probability that x lies between 9 and 22 is given by :-
[tex]=\dfrac{13}{24}[/tex]
