An experiment is designed to test the potency of a drug on 40 rats. Previous animal studies have shown that a 10-mg dose is lethal 10% of the times within the first 4 hours. What is the probability that between 2 and 8 rats die during the experiment due to the drug?
Alice Chen
Answered question
2022-11-14
What is the probability that between 2 and 8 rats die during the experiment due to the drug?
My attempt: Let X be the number of rats that die in the first 4 hours.
To make the drug more potent, the company came with a new formula. This reduced the chances of a new drug being lethal to 1%. The new drug is administered to 10000 rats. Approximate the exact probability that 5 rats die.
My attempt:
Am I on the right path?
Answer & Explanation
Haylie Park
Beginner2022-11-15Added 14 answers
We can utilize some small python script as it is kind of hard by hand.
from scipy import stats
# number of rats
n=40
# lethal dose probability
p=.1
# upper bounds
kmax = 8
kmin = 1
# cdf summations
y1 = stats.binom.cdf(kmin, n, p)
y2 = stats.binom.cdf(kmax,n,p)
# differences
y = y2-y1
y
y
Out[13]: 0.9040309985710783
Note the binom.cdf command is
So we to set our limits
then we find
there is a 90% chance 2 - 8 rats die.
ok..the second one
from scipy import stats
# number of rats
n=10000
# lethal dose probability
p=0.01
# exact number
k = 5
# pmf
y = stats.binom.pmf(k, n, p)
y
Out[8]: 1.968586020940221e-36
Wow, startling difference.. I don't think you can do these by hand. You can make rough approximations.
In the last equation you get some rough terms...
Various things will drop out
It just becomes a really small number..this is the exact reason calculators were invented.
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