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.

goog may have it for you

the answer would be d.

step-by-step explanation:

move all variables to the left side and all constants to the right side

(x−3)^2+(y−1)^2=16

this is the form of a circle. use this form to determine the center and radius of the circle.

( x − h ) 2 + ( y − k ) 2 = r 2

match the values in this circle to those of the standard form. the variable   r   represents the radius of the circle,   h   represents the x-offset from the origin, and   k   represents the y-offset from origin.

r = 4

h = 3

k = 1

the center of the circle is found at   ( h , k ) .

center:   ( 3 , 1 )

these values represent the important values for graphing and analyzing a circle.

center:   ( 3 , 1 ).

radius:   4