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

Answer:

$P(Y=0) = 0.1353$

Step-by-step 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

 $\lambda=\frac{1}{E(X)}$

 $\lambda=\frac{1}{5}$

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

 $P(Y=0) = \frac{e-2 (2)0}{0!}$

 $P(Y=0) = e-2$

 $P(Y=0) = 0.1353$