researchers conducted a study to determine whether there were significant differ

Question

researchers conducted a study to determine whether there were significant differences in graduation rates between medical students admitted through special programs and medical students admitted through regular admissions criteria it was found that the graduation rate was 96% for the medical students admitted through special programs in all medical schools complete A & B below if 15 of the students admitted through special programs are randomly selected find the probability that at least 14 of them graduated the probability that 14 of the 15 students graduated is

Explanation / Answer

n = 15 , p = 0.96

As per binomial distribution,
P(X=r) = nCr * p^r * (1-p)^(n-r)

P(x > =14) = P(x = 14) + P(x =15)
= 15C14 * 0.96^14 * ( 1-0.96)^1 + 15C15 * 0.96^15 * ( 1-0.96)^0

= 0.3388 + 0.5421

= 0.8809

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