Problema Solution
A drug tester claims that a drug cures a rare skin disease?
72% of the time. The claim is checked by testing the drug on 100 patients. If at least 66 patients are cured the claim will be accepted.
Answer provided by our tutors
ANSWER: PROBABILITY = 92.3990% likely at least 66 patients will be cured
Why???
BINOMIAL DISTRIBUTION, POPULATION PROPORTION
n = NUMBER OF TRIALS [ 100] (sample size)
k = NUMBER OF SUCCESSES [65] (from 0 up to and including k NUMBER OF SUCCESSES)
p = POPULATION PROPORTION [72%]
significant digits6
COMPUTATION OF BINOMIAL PROPORTION:
P(k=>66) = 1 - P(k ? 65) = 1 - n!/[k!*(n - k)!] * p^k * (1 - p)^(n - k) = 1 - 100!/[65!*(100 - 65)!] * 0.72^65 * (1 - 0.72)^(100 - 65) = 1 - 0.076010 = 0.923990
ALTERNATIVE COMPUTATION USING EXCEL:
Look-up value of PROBABILITY = 1 - BINOMDIST ( 65 , 100 , 72/100 , TRUE )
Using Excel function: BINOMDIST(number_s, trials, probability_s, cumulative)
Number_s is the number of successes in trials. [ 100 ]
Trials is the number of independent trials. [ 65 ]
Probability_s is the probability of success on each trial. [ 72]
Cumulative is a logical value that determines the form of the function. If cumulative is TRUE, then BINOMDIST returns the cumulative distribution function, which is the probability that there are at most number_s successes; if FALSE, it returns the probability mass function, which is the probability that there are number_s successes.