Question 15 (8 pointe): A wildlife biologist examines frogs for a gemetic trait

Question

Question 15 (8 pointe): A wildlife biologist examines frogs for a gemetic 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 i-pproximately 15% of frogs. He examines ten randomly sected frogs. Let X be the number of frogs that have the trait among the te 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 X7 (e) Find the mean ux and standard deviation ox of the mumber of bop with the trait. (d) Compute the probability that at mont one of the wilected trog will have the particular genetic trait. (e) Suppose that the random variables ? '.. ..xe flow the sne 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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