Question 16 (8 pointa): A wildlife biologist examines frogs for a gemeti trait h

Question

Question 16 (8 pointa): A wildlife biologist examines frogs for a gemeti trait he suspects may be linked to sensitivity to industrial toncins in the environment. Previous research had established that this trait is usually found in approximately 15% of frogs. He examines ten randomly selected frogs. Let X be the number of frogs that have the trait among the ten collected frogs and assume that a frog will have the particular genetic trait with a probability of 0.15. (a) Give the range of the random variable X (b) What is the distribution of X? (c) Find the mean ,1x and standard deviation ?x of the number of frogs with the trait. Compute the probability that at most one of the selected frogs will have the particular genetic trait. (d) (e) Suppose that the random variables X,..., X follow the same distri- bution of X (in (b)). Compute P (X

Explanation / Answer

a)

X can takes values 0 , 1 ,2,...10

b)
X follows binomial distribution
with n = 10 , p = 0.15

c)
mean = np = 1.5
sd =sqrt(npq) = sqrt(10*0.15*0.85) = 1.12915897906

d)
P(X <= 1) = P(X = 0) + P(X - 1)
P(X = k) = nCk p^k q^(n-k)

P(X< =1) = q^10 + 10* p q^9
= 0.85^10+ 10 * 0.15 * 0.85^9
= 0.54429982376

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