Question

If the average number of potholes per mile in a given city is 10, what is the probability that a randomly selected mile will have 10 or fewer potholes?

Answer 1

Answer:

Answer and Explanation:

a. For a quarter-mile stretch, the parameter is

λ=1/4×12=3

The probability mass function is p(x,3)=

e−3⋅3xx!.

The probability of finding fewer than two potholes is given by P(X<2)

=p(0,3)+p(1,3).P(X<2)=p(0,3)+p(1,3)P(3<2)=e−3+3e−3=4e−3≈0.1991

b. The probability of finding more than one pothole in a quarter-mile stretch of highway is

P

(

X

>

1

)

=

P

(

X

≥

2

)

=

1

−

P

(

X

<

2

)

.

From part a,

P

(

X

<

2

)

=

4

e

−

3

.

P

(

X

>

1

)

=

1

−

4

e

−

3

=

0.8809