In testing a new drug to combat a common illness it was found that 75% of the pa

Question

In testing a new drug to combat a common illness it was found that 75% of the patients to whom the drug was administered experienced a reduction in symptoms. What is the probability that in a group of 20 people afflicted with the ailment

            A. at least 15 find some relief?

            B. more than 17 experience improved conditions?

            C. less than 10 benefit from the drug?

            D. less than 8 but more than 5 are helped?

            E. at least 14 are helped?

            F. If the mean number of people is greater than 12 The National Health Service (NHS) will fund further research. Is the additional funding forthcoming?

           G. The NHS wishes to keep the standard deviation in the number of patients who benefit from the drug to less than 2. Is this condition maintained

Explanation / Answer

N=20 ,p=0.75

a) P( at least 15) = P(15+16+17+18+19+20)=0.5851 using binomial calculator on TI-84

b)P( more than 17)=0.2251

c)P= 0.01386441694376117

d)P(atleast 14)=Atleast 15+ 14 = 0.5851+0.1686=0.7857

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