# Answer to Question #2826 in Statistics and Probability for alyssa

Question #2826

20% of the deer in a wildlife preservation part are believed to have certain antler infections. A zoologist randomly captures 15 deer and checks their antlers. Assuming the prediction is accurate, determine the probability that more than three of the deer will have infected antlers.

Expert's answer

The number X of deers among n=15 ones having infected antlers has binomial distribution with parameters

p=0.2, q=1-p=0.8,

so

P(X=m) = C(15, m) 0.2

Hence

P(X>3) = 1-P(X<4) = 1- P(X=0) - P(X=1) - P(X=2) - P(X=3) =

= 1- 0.8

= 1 - 0.03518 - 0.13194 - 0.23090 - 0.25014 = 0.35184

p=0.2, q=1-p=0.8,

so

P(X=m) = C(15, m) 0.2

^{m}0.8^{(15-m)}Hence

P(X>3) = 1-P(X<4) = 1- P(X=0) - P(X=1) - P(X=2) - P(X=3) =

= 1- 0.8

^{15}- 15∙0.2∙0.8^{14}- (15∙14)/2∙0.2^{2}∙0.8^{13}- (15∙14∙13)/(2∙3)∙0.2^{3}∙0.8^{12}== 1 - 0.03518 - 0.13194 - 0.23090 - 0.25014 = 0.35184

Need a fast expert's response?

Submit orderand get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

## Comments

## Leave a comment