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Answer:
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.