On average, there are 12 potholes per mile on a particular stretch of the state highway. Suppose the potholes follow a Poisson distribution on the highway. a. Find the probability of finding fewer than two potholes in a quarter-mile stretch of the highway. (Do not round intermediate calculations. Round your final answer to 4 decimal places.) b. Find the probability of finding more than one pothole in a quarter-mile stretch of the highway. (Do not round intermediate calculations. Round your final answer to 4 decimal places.)

a) 0.1992 = 19.92% probability of finding fewer than two potholes in a quarter-mile stretch of the highway.

b) 0.8008 = 80.08% probability of finding more than one pothole in a quarter-mile stretch of the highway.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

In which

x is the number of sucesses

e = 2.71828 is the Euler number

is the mean in the given interval.

a. Find the probability of finding fewer than two potholes in a quarter-mile stretch of the highway.

Mean of 12 potholes per mile, which means that in a quarter-mile stretch, the mean is

This probability is:

In which

0.1992 = 19.92% probability of finding fewer than two potholes in a quarter-mile stretch of the highway.

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

This is

We have that

So

0.8008 = 80.08% probability of finding more than one pothole in a quarter-mile stretch of the highway.

25/6

step-by-step explanation:

you multiply 4 by the denominator (4*6=24) and add it to the numerator which makes it 25/6.

your answer is

a.

5

step-by-step explanation: