Question

You are working in a lab and the PI gives you a polypeptide that is 500 amino acids in length. You are studying a disease wherein a change in amino acid sequence results in an inability to achieve proper enzyme/substrate binding. A new drug has been synthesized that aids in the proper binding process. A study performed on the drug has shown that the drug works in 40% of patients. Approximate all of the following using the Gaussian distribution.

a. If 15,000 people affected by the disease are given the drug, estimate the number of patients who will be symptom free as a result of proper binding.

b. Estimate the probability that of the 15,000 affected who receive the drug, no one reports symptoms of the disease.

c. Estimate the probability that of the 15,000 affected who receive the drug, 8,500 report experiencing symptoms.

Answer 1

Given

Probability of drug working =p=0.4

A)

Given n=15000

So

Estimate of peoples who will become drug free=n*p=15000*0.4=6000

B)

Let X is no.of person who report symptomp of dieses so

Here

Probability=q=1-p=1-0.4=0.6

And n=15000

So X~bin(15000,0.6)

We have to find P(X<0)=?

So E(X)=n*q=15000*0.6=9000

Var(X)=n*p*q=15000*0.4*0.6=3600

So SD(X)=60

Now

c)

We have to find P(X=8500)=P(X<8500)- P(X<8400)

Now using all data from.part B

=P(Z<-8.333)-P(Z<-8.35)=0-0=0