Answer:
[tex]P(Y=0) = 0.1353[/tex]
Step-by-step explanation:
From the question we are told that:
Exponential distribution mean [tex]\=x = 5 miles[/tex]
Distance [tex]d=10miles[/tex]
Generally the equation for Exponential distribution is mathematically given by
[tex]\lambda=\frac{1}{E(X)}[/tex]
[tex]\lambda=\frac{1}{5}[/tex]
Therefore
Possion Y
[tex]10\lambda=10*(1/5)[/tex]
[tex]10\lambda=2[/tex]
Generally the equation for The probability that there are no major cracks in a 10 mile stretch of the highway is mathematically given by
[tex]P(Y=0) = \frac{e-2 (2)0}{0!}[/tex]
[tex]P(Y=0) = e-2[/tex]
[tex]P(Y=0) = 0.1353[/tex]
