Question

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.

Answer 1

Answer:

P [ 4 <  x  <  5 ]  = 0,0788      or   7,88 %

Step-by-step explanation:

We are going to solve an exponentially distributted problem

as μ = 6   then     λ = 1/6

We 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 excel

P [ 4 <  x  <  5 ]  =  0,5134 - 04346

P [ 4 <  x  <  5 ]  = 0,0788      or   7,88 %