A car painting company has determined that the painting time of cars is uniformly distributed between 25 and 105 minutes. What is the probability that it will take between 40 and 65 minutes for that company to paint a car

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 minWe 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]