Help Needed! Specifically, What is the probablity that 8 will survive? Albino ra
ID: 3332257 • Letter: H
Question
Help Needed! Specifically, What is the probablity that 8 will survive?
Albino rats used to study the hormonal regulation of a metabolic pathway are injected with a drug that inhibits body synthesis of protein. The probability that a rat will die from the drug before the experiment is over is 2. If 10 animals are treated with the drug, how many are expected to die before the experiment ends? What is the probability that at least eight will survive? Would you be surprised if at least five died during the course of the experiment? Explain, based on the probability of this occurringExplanation / Answer
BIONOMIAL DISTRIBUTION
pmf of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
where
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial
I.
mean = np
where
n = total number of repetitions experiment is excueted
p = success probability
mean = 10 * 0.2
= 2
II.
variance = npq
where
n = total number of repetitions experiment is excueted
p = success probability
q = failure probability
variance = 10 * 0.2 * 0.8
= 1.6
III.
standard deviation = sqrt( variance ) = sqrt(1.6)
=1.2649
probability that atleast 8 will survive
P( X < 8) = P(X=7) + P(X=6) + P(X=5) + P(X=4) + P(X=3) + P(X=2) + P(X=1) + P(X=0)
= ( 10 7 ) * 0.2^7 * ( 1- 0.2 ) ^3 + ( 10 6 ) * 0.2^6 * ( 1- 0.2 ) ^4 + ( 10 5 ) * 0.2^5 * ( 1- 0.2 ) ^5 + ( 10 4 ) * 0.2^4 * ( 1- 0.2 ) ^6 + ( 10 3 ) * 0.2^3 * ( 1- 0.2 ) ^7 + ( 10 2 ) * 0.2^2 * ( 1- 0.2 ) ^8 + ( 10 1 ) * 0.2^1 * ( 1- 0.2 ) ^9 + ( 10 0 ) * 0.2^0 * ( 1- 0.2 ) ^10
= 0.9999
P( X > = 8 ) = 1 - P( X < 8) = 0.0001
probability that atleast 5 died during the experiment
P( X < 5) = P(X=4) + P(X=3) + P(X=2) + P(X=1) + P(X=0)
= ( 10 4 ) * 0.2^4 * ( 1- 0.2 ) ^6 + ( 10 3 ) * 0.2^3 * ( 1- 0.2 ) ^7 + ( 10 2 ) * 0.2^2 * ( 1- 0.2 ) ^8 + ( 10 1 ) * 0.2^1 * ( 1- 0.2 ) ^9 + ( 10 0 ) * 0.2^0 * ( 1- 0.2 ) ^10
= 0.9672
P( X > = 5 ) = 1 - P( X < 5) = 0.0328
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