Question

An experiment is designed to test the potency of a drug on 10 rats. Previous animal studies have shown that a 10-mg dose of the drug is lethal 5% of the time.

a) What is the probability that exactly 2 rats will die?

b) What is the probability that exactly 0 rats will die?

c) What is the probability that 3 or more rats will die?

d) What is the mean (or the expected number of deaths) and standard deviation for this probability distribution?

Answer 1

Answer)

Answer)

Here we need to use the binomial formula

P(r) = ncr*(p^r)*(1-p)^n-r

Ncr = n!/(r!*(n-r)!)

N! = N*n-1*n-2*n-3*n-4*n-5........till 1

For example 5! = 5*4*3*2*1

Special case is 0! = 1

P = probability of single trial = 0.05 (5%)

N = number of trials = 10

R = desired success

A)

P(2)

After substitution

Required probability is 0.07463479852

B)

P(0) = 0.59873693924

C)

P(3 or more) = p(3) + p(4) + ....

We know that sum of all the probabilities is = 1

So, p(3 or more) = 1 - (p(0) + p(1) + p(2))

= 0.01150355738

D)

Mean = n*p = 10*0.05 = 0.5

S.d = √n*p*(1-p) = 0.68920243760