Question

The distance between major cracks in a highway follows an exponential distribution with a mean of 13 miles. What is the standard deviation of the distance between two major cracks? Please enter the answer to 2 decimal places.

Answer 1

σ = 13 miles

Explanation:

Let us consider X continuous random variable and λ be the parameter of exponential density function.

where E(x) =
`(1)/(\lambda)`

where E(x) = is expected value=13

we have to find λ=
`(1)/(E(x))`

λ=
`(1)/(13)`

λ=0.076

standard deviation = V(X) = σ =
`(1)/(\lambda)`

now , σ =
`(1)/(0.076)`

σ = 13 miles is the distance between the two major crack.