In a region, there is a 0.9 probability chance that a randomly selected person o

Question

In a region, there is a 0.9 probability chance that a randomly selected person of the population has brown eyes. Assume 13 people are randomly selected. Complete parts (a) through (d) below. a. Find the probability that all of the selected people have brown eyes. The probability that all of the 13 selected people have brown eyes is. b. Find the probability that exactly 12 of the selected people have brown eyes. The probability that exactly 12 of the selected people have brown eyes is. c. Find the probability that the number of selected people that have brown eyes is 11 or more. The probability that the number of selected people that have brown eyes is 11 or more is. d. If 13 people are randomly selected, is 11 an unusually high number for those with brown eyes? A. No, because the probability that 11 or more of the selected people have brown eyes is greater than 0.05. B. No, because the probability that 11 or more of the selected people have brown eyes is less than 0.05. C. Yes, because the probability that 11 or more of the selected people have brown eyes is greater than 0.05. D. Yes. because the probability that 11 or more of the selected people have brown eyes is less than 0.05.

Explanation / Answer

Let X be the random variable denoting the number of people who have brown eyes. X follows a binomial distribution with parameters n=13 and p=0.9

a) P(X=13)= (13C13)*(0.9^13)*((1-0.9)^(13-13))
=0.254
excel command : =BINOMDIST(13,13,0.9,FALSE)

b) P(X=12)= (13C12)*(0.8^12)*((1-0.8)^(13-12))
=0.367
excel command : =BINOMDIST(12,13,0.9,FALSE)

c)P(X>=11)=1-P(x<=10)

=1- =BINOMDIST(10,13,0.9,FALSE)

=0.900

d) Option A is correct.

Hope this will helpful. Thanks God Bless you :)

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