SOLUTION: Poisson Distribution. A healthy female rabbit typically produces an average of seven litters per year. Suppose that one healthy female rabbit is randomly chosen. Fill in “Tru

Question 1187527: Poisson Distribution. A healthy female rabbit typically produces an average of seven litters per year. Suppose that one healthy female rabbit is randomly chosen.
Fill in “True” or “False”: The random variable X represents the number of litters per year that a healthy female rabbit can have.
Fill in “True” or “False”: X may not take on whole number values 0, 1, 2, 3, …
The probability (in % terms) that she has exactly on litter in one year is
%. (round to two decimals)
The probability (in % terms) that she has at least two litters in one year is
%. (round to two decimals)
The probability (in % terms) that she has exactly three litters in one year is
%. (round to two decimals)
The probability (in % terms) that she has between 2 and 4 litters in one year is
%. (round to two decimals)
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
True
False--X must take on whole number values in this instance. Mathematically it does not have to, but with litters, there are no fractional ones.
-
e^(-7)*7^1/1!=0.0064, or 0.01
confirm with Poissonpdf(7,1) ENTER
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we know that 1 litter has probability 0.0064 and 0 is e^(-7)=0.0009. They add to 0.0073, and the complement or 0.9927, is the answer, at least two litters. Two decimal places is 0.99
-
exactly 3 litters is e^(-7)*7^3/3!=0.0521, or 0.05
-
exactly 4 litters is e^(-7)*7^4/24=0.0912, or 0.09
so the answer is that plus 0.0521 and the probability of 2 litters (0.0223)=0.1656, or 0.17
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