Assume that in a large population of frogs, 45% are infected with the chytrid fu

Question

Assume that in a large population of frogs, 45% are infected with the chytrid fungus. If a random sample of 8 frogs is chosen then: a.) What is the probability that 5 of these frogs will be so infected? b.) What is the probability that two or more will be infected? c.) What is the probability that more than two will be infected? 9. For problem #8 above, calculate the following: a.) Mean b.) Variance c) Standard Deviation 10. For problem #8 above, calculate k, the integer that would yield the highest probability.

Explanation / Answer

Probability that a frog is infected, p = 0.45

As per binomial distribution,
P(X=r) = nCr * p^r * (1-p)^(n-r)

a)
P(X=5) = 0.45^5 = 0.0185

b)
P(X >= 2) = 1 - P(X<=1)
= 1 - P(X = 0) - P(X=1)
= 1 - 0.55^5 - 5*0.45*0.55^4
= 0.7438

c)
P(X>2) = 1 - P(X<=2)
= 1 - P(X = 0) - P(X=1) - P(X=2)
= 1 - 0.55^5 - 5*0.45*0.55^ - 5C2*0.45^2*0.55^3
= 0.4069

#9.
a) Mean = 5*0.45 = 2.2500
b) variance = 5*0.45*0.55 = 1.2375
c) std. dev. = sqrt(variance) = 1.1124

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.