Question

The distance between major cracks in a highway follows an exponential distribution with a mean of 5 miles. (a) What is the probability that there are no major cracks in a 10-mile stretch of the highway

Answer 1

`P(Y=0) = 0.1353`

Explanation:

From the question we are told that:

Exponential distribution mean
`\=x = 5 miles`

Distance
`d=10miles`

Generally the equation for Exponential distribution is mathematically given by

`\lambda=(1)/(E(X))`

`\lambda=(1)/(5)`

Therefore

Possion Y

`10\lambda=10*(1/5)`

`10\lambda=2`

Generally the equation for The probability that there are no major cracks in a 10 mile stretch of the highway is mathematically given by

`P(Y=0) = (e-2 (2)0)/(0!)`

`P(Y=0) = e-2`

`P(Y=0) = 0.1353`