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The probability that a mouse inoculated with a serum will
Chapter 3, Problem 137E(choose chapter or problem)
Problem 137E
The probability that a mouse inoculated with a serum will contract a certain disease is .2. Using the Poisson approximation, find the probability that at most 3 of 30 inoculated mice will contract the disease.
Questions & Answers
QUESTION:
Problem 137E
The probability that a mouse inoculated with a serum will contract a certain disease is .2. Using the Poisson approximation, find the probability that at most 3 of 30 inoculated mice will contract the disease.
ANSWER:
Solution :
Step 1 of 2:
Given the probability that a mouse inoculated with a serum will contract a certain disease is 0.2.
Using the poisson distribution we have to find the probability that at most 3 of 30 inoculated mice will contract the disease.
Here n=30 and p=0.2.
Our goal is:
We need to find the probability that at most 3 of 30 inoculated mice will contract the disease.
The average rate is the product of the sample size and the probability is
=
=
=
Hence is 6.
Then the formula of the poisson probability is
P(X=k)=