Sections 4.2.43. 44, 52&53 in a region, there is a 0 95 probability chance that

Question

Sections 4.2.43. 44, 52&53 in a region, there is a 0 95 probability chance that a randomly selected person of the popuistion has brown Assume 10 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 10 selected people have brown eyes s Round to three decimal places as needed) b. Find the probability that exactly 9 of the selected people have brown eyes The probability that exactly 9 of the selected people have brown eyes s Round to three decimal places as needed) c. Find the probability that the number of selected people that have brown eyes is 8 or more The probability that the number of selected people that have brown eyes is 8 or more (Round to three decimal places as needed) d. If 10 people are randomly selected, is 8 an unusually high number for those with brown eyes A. Yes, because the probability that 8 or more of the selected people have brown eyes is less than 0 05 e B. No because the probability that 8 or more of the selected people have brown eyes is greater the C. 985 because the probability that 8 or more of the selected people have brown eyes is greater than 0 05 D. No, because the probability that 8 or more of the selected people have brown eyes s less than 0

Explanation / Answer

Binomial distribution

p = 0.95

q = 1 - p = 0.05

n = 10

P(X) = nCx px qn-x

a) P(all the selected people have brown eyes) = P(10)

= 0.9510

= 0.5987

b) P(9 of the selected people have brown eyses) = P(9)

= 10 x 0.959 x 0.05

= 0.3151

c) P(8 or more have brown eyes) = P(8) + P(9) + P(10)

= 10C8 x 0.958 x 0.052 + 0.3151 + 0.5987

= 0.0746 + 0.3151 + 0.5987

= 0.9884

d) B. No, because the probability that 8 or more of the selected people have brown eyes is greater than 0.05

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