Suppose the time a child spends waiting at for the bus as a school bus stop is exponentially distributed with mean 6 minutes. Determine the probability that the child must wait between 4 and 5 minutes on the bus on a given morning.
Accepted Solution
A:
Answer:P [ 4 < x < 5 ] = 0,0788 or 7,88 %Step-by-step explanation:We are going to solve an exponentially distributted problemas μ = 6 then λ = 1/6We are looking for the probability of:P [ 4 < x < 5 ]That probability is equal to:P ( x < 5 ) - P ( x < 4 ) (1)P ( x < 5 ) = 1 - е∧( -1/6)(5) ⇒ 1 - е∧ (- 5/6)and P ( x < 4 ) = 1 - е∧( -1/6)(4) ⇒ 1 - е∧ (- 4/6)By substitution in equation (1) P [ 4 < x < 5 ] = 1 - е∧ (- 5/6) - [1 - е∧ (- 4/6)]P [ 4 < x < 5 ] = е∧ (- 4/6)] - е∧ (- 5/6)Solving with excelP [ 4 < x < 5 ] = 0,5134 - 04346P [ 4 < x < 5 ] = 0,0788 or 7,88 %