The number of field mice found in a wheat field follows a Poission process. If the average number of field mice in a 5-acre wheat field is estimated to be 12. Find the probability that (a) fewer than 3 field mice are found on a given acre. (b) in 2 of the next 3 acres inspected, fewer than 3 field mice are found on each acre.

a) 56.97% probability that fewer than 3 field mice are found on a given acre.

b) 41.90% probability that in 2 of the next 3 acres inspected, fewer than 3 field mice are found on each acre.

Step-by-step explanation:

To solve this question, we use the Poisson probability distribution and the binomial probability distribution.

Poisson distribution:

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 time interval.

Binomial distribution:

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

If the average number of field mice in a 5-acre wheat field is estimated to be 12.

Find the probability that

(a) fewer than 3 field mice are found on a given acre.

5 acres have a mean of 12. For one acre

This probability is

In which

56.97% probability that fewer than 3 field mice are found on a given acre.

(b) in 2 of the next 3 acres inspected, fewer than 3 field mice are found on each acre.

Here we use the binomial probability distribution.

56.97% probability that fewer than 3 field mice are found on a given acre, which means that

This probability is P(X = 2) when n = 3.

41.90% probability that in 2 of the next 3 acres inspected, fewer than 3 field mice are found on each acre.

a is the correct

the weight of the object inside the box!