Question-85

cdf
uniform

A package delivery time \(T\) (in hours) is uniformly distributed over the interval \([ a,b]\). It is known that the probability that the delivery takes less than \(5\) hours is equal to the probability that it takes more than \(11\) hours. Find \(a+b\).

\(16\)

We are given that \(P( T< 5) =P( T >11)\) where \(T \sim U[a, b]\). From this, we have:

\[ \begin{aligned} \frac{5-a}{b-a} & =\frac{b-11}{b-a}\\ 5-a & =b-11\\ a+b & =16 \end{aligned} \]