Question-28
The total duration of a Test cricket match between any two cricket team is uniformly distributed between 30 hours and 40 hours, both inclusive. What is the \(65^{th}\) percentile for the duration of a test cricket match between any two cricket team in hours?
If \(X \sim \text{Uniform}[a,b]\), then \(E(X) = \dfrac{a+b}{2}\) and \(Var(X) = \dfrac{(b-a)^{2}}{12}\). Also,
\(F(x) = P(X \leq x) = \dfrac{x-a}{b-a}\)
\(65^{th}\) percentile denotes the value of \(k\) for which \(P(X \leq k) = 0.65\).
36.5
According to the question \(X \sim \text{Uniform}[30, 40]\).
\(65^{th}\) percentile denotes the value of \(k\) for which \(P(X \leq k) = 0.65\).
\(\dfrac{k-30}{40-30} = 0.65 \implies \dfrac{k-30}{10} = 0.65\)
\(\implies k - 30 = 10 \times 0.65\)
\(\implies k - 30 = 6.5 \implies k = 36.5\)