SOLUTION: A biologist estimates that 40% of the deer in a region carry a certain type of tick. For a sample of 300 deer selected at random, what is the chance that 124 or fewer deer have thi

Question 1085611: A biologist estimates that 40% of the deer in a region carry a certain type of tick. For a sample of 300 deer selected at random, what is the chance that 124 or fewer deer have this tick?

A. 0.864

B. 0.702

C. 0.404

D. 0.298

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
Use the binomial distribution formula
:
p = 0.40, n = 300, r varies from 0 to 124
:
Probability (P) ( r successes out of 300 ) = 300Cr * (0.40)^300 * (1-0.40)^(300-r)
:
Note 300Cr = 300! / (r! * (300-r)!)
:
then sum the P(r)'s
:
fortunately there are binomial distribution calculators, therefore
:
P ( 124 or fewer deer are infected ) = 0.7030 approximately 0.70 or 70%
:
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answer is B.
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