Answer:
[tex]P=\frac{5}{16}[/tex]
Step-by-step explanation:
For a uniform distribution we have to:
[tex]P (X\leq x) =\frac{x-a}{b-a}[/tex] for x∈ (a, b)
[tex]P (X\leq x) =0}[/tex] for [tex]x\leq a[/tex]
[tex]P (X\leq x) =1}[/tex] for [tex]x\geq b[/tex]
In this case we have to:
a = 25 min and b = 105 min
We want to find:
[tex]P (40 \leq X \leq 65)[/tex]
Then
[tex]P (x_1 \leq X \leq x_2) = P(X \leq x_2) - P(X \leq x_1)[/tex]
[tex]P (x_1 \leq X \leq x_2)= \frac{x_2 -x_1}{b-a}[/tex]
In this case:
[tex]x_2 = 65\\\\x_1=40[/tex]
Therefore:
[tex]P (40 \leq X \leq 65)=\frac{65 -40}{105-25}[/tex]
[tex]P (40 \leq X \leq 65)=\frac{25}{80}[/tex]
[tex]P (40 \leq X \leq 65)=\frac{5}{16}[/tex]
