Question

In a? region, there is a 0.8 probability chance that a randomly selected person of the population has brown eyes. Assume 12 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 12 selected people have brown eyes is.

?(Round to three decimal places as? needed.)

b. Find the probability that exactly 11 of the selected people have brown eyes.

The probability that exactly 11 of the selected people have brown eyes is.

?(Round to three decimal places as? needed.)

c. Find the probability that the number of selected people that have brown eyes is 10

or more.

The probability that the number of selected people that have brown eyes is 10 or more is.

?(Round to three decimal places as? needed.)

d. If 12 people are randomly? selected, is 10 an unusually high number for those with brown?eyes?

A. No?, because the probability that 10 or more of the selected people have brown eyes is less than 0.05.

B. Yes?, because the probability that 10 or more of the selected people have brown eyes is less than 0.05.

C. No?, because the probability that 10 or more of the selected people have brown eyes is greater than 0.05.

D. Yes?, because the probability that 10 or more of the selected people have brown eyes is greater than 0.05.

Answer 1

Here n=12, p=0.8.

X: The number of people selected have brown eyes.

X~Binomial(n=12,p=0.8)

(a) The probability that all of the 12 selected people have brown eyes is P(X=12)= (0.8)¹²=0.0687.

(b) The probability that exactly 11 of the selected people have brown eyes is.

  

(c) The probability that the number of selected people that have brown eyes is 10 or more is

(d)   No, because the probability that 10 or more of the selected people have brown eyes is greater than 0.05.