In a region, there is a 0.8 probability chance that a randomly selected person o

Question

In a region, there is a 0.8 probability chance that a randomly selected person of the population has brown eyes. Assume 14 people are randomly selected. Complete parts (a) through (d) belvw. a. Find thc pr of e scected peopk: have brown cyes The obabity that all probability that all of the 14 selected people have brown eyes is found to three decimal pieces as needed.) b. Find the probability that exactly 13 of the selected people have brown eyes. The probability that exactly 13 ot the selected people have brown eyes is Round to three decimal places as needed.) c. Find the probabiity thet the number of selected people thst have brown eyes is 12 or more The probability that the number of selected people thal have brown eyes is 12 or more is Round to three decimal places as neededy d. I 14 people are randomly selerted is 12 an unusally high number for those with by? A. No, becauseprobability ity| 12 urrmee or the selocled peuplo have blown Bybs is greale' ter' 0.05 O B. Yes, because the probability that 12 or more of the selected people have brown eyes is less than 0.05. lhar 0.05 C. O D. Yes, because the probability that 12 or more ofthe selected people have brown eyes is greater than 0.05. No, because the probability that 12 or more ofthe selected people have brown eyes is less than 0.05. Click to select your answers).

Explanation / Answer

Solution:-

p = 0.80

n = 14

a) The probability that all of the selected people have brown eyes is 0.04398.

x = 14

By applying binomial distribution

P(x,n) = nCx*px*(1-p)(n-x)

P(x = 14) = 0.04398

b) The probability that exactly 13 of the selected people have brown eyes is 0.1539.

x = 13

By applying binomial distribution

P(x,n) = nCx*px*(1-p)(n-x)

P(x = 13) = 0.1539

c) The probability that number of the selected people have brown eyes is 12 or more is

x = 12

By applying binomial distribution

P(x,n) = nCx*px*(1-p)(n-x)

P(x > 12) = 0.4481

d) (A) No, because the probability that 12 or more of the selected poeple have brown eyes is greater than 0.05.

P(x = 12) = 0.2501

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