Question

A drug trial involves 75 patients. At the time the efficacy of the drug is unknown, but many years later researchers will find that it cures 55% of patients. Let X denote the number who are cured (a) Find the mean and standard deviation of X (b) Use the Empirical Rule to fill in the blanks, and then add work: "There is a 2/3 chance that the drug trial will find between % and % are cured."

Answer 1

Given, patients n=75 Probability that it cures p=55% = 0.55 Let X follows number who cured X follows binomial distribution and size is more, it tends to normal with a) Mean u=np = 75*0.55 = 41.25 Standard deviation o npq = 775 * 0.55 +0.45 = 4.3084~4.31 b) According to empirical rule of probability 68% of data lies between 4-0 and uto 1-0 = 41.25-4.31 =36.94 H+0 = 41.25 +4.31 =45.56 There is 2/3 (67%) chance that drug trail lies between 36.94% and 45.56% are cured