Take a Test-Olivia N rt 1621 MAT181-805 Statistics I Test: TEST-2 Submit Test Th

Question

Take a Test-Olivia N rt 1621 MAT181-805 Statistics I Test: TEST-2 Submit Test This Question: 1 pt This Test: 15 pts In a region, there is a 0.95 probability chance that a randomly selected person of the population has brown eyes. Assume 12 people are randormly selected Complete parts (a) through (d) below. The probability that exactly 11 of the selected people have brown eyes is 0341 (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? 0 A. No, because the O B. No, because the probablity that 10 or more of the selected people have brown eyes is greater than 0 05 because the probabiliy that 10 or more of the selected people have brown eyes is less than 0 05 because the probability that 10 or more of the selected people have brown eyes is less than 0.05 0.05 C. Yes, because the probability that 10 or more of the selec O D. Yes, because the probability that 10 or more of the selected people have brown eyes is greater than 0.05

Explanation / Answer

Given

The probability that a person have brown eyes is (p) = 0.95

then q= 0.05

n = 12

b) the probability that exactly 11 of the selected people have brown eyes ?

this is a binomial distribution of P(X=11)

hence the probability that exactly 11 of the seclected people have brown eyes = 12C11 * 0.95^11 * 0.05^1

=12 * 0.95^11 * 0.05

=0.3412

c)probability that selected persons are 10 or more?

10 or more persons means we have to calculate the probability for p(x=10) + p(x=11) + p(x=12)

p(x=10) = 12C10 * 0.95^10 * 0.05^2

= 66 * 0.95^10 * 0.05^2

=0.0987

p(x=11) =12C11 * 0.95^11 * 0.05^1

=12 * 0.95^11 * 0.05

=0.3412

p(x=12) = 12C12 *0.95^12 *0.05^0

=0.95^12

=0.540

summing up all these we get the probability that 10 or more persons have brown eyes

=p(x=10)+p(x=11)+p(x=12)

=0.0987 + 0.3412 + 0.540

=0.9799

approximately 0.98

c)

this is not unusual since the probability that 10 or more have brown eyes is far greater than 0.05

hence option 2 is correct

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