Question

Suppose the event of a student’s application to a university being accepted follows the binomial probability. The successful rate is 80%. Please finish the following tasks? (1) Determine the expected number of acceptances for the next nine applicants and the standard deviation. (2) What is the probability that among the next 10 applicants exactly 6 will be accepted?

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Answer 1

Answer:

Given,

Binomial distribution P(X = x) = nCr*p^r*q^(n-r)

sample n = 9

p = 80% = 0.8

q = 1 - p

= 1 - 0.8

= 0.2

Expected number = np

= 9*0.8

= 7.2

Standard deviation = sqrt(npq)

= sqrt(9*0.8*0.2)

= 1.2

b)

P(X = 6) = 10C6*0.8^6*0.2^(10-6) [nCr = n!/(n-r)!*r!]

= 210*0.8^6*0.2^4

= 0.0881