Question

Based on a previous known-fate survival study, you believe that yearly survival for a species is 0.65. Assuming that this estimate is the true survival of a population if you have 43 animals fitted with radio-telemetry:

a) What is the appropriate distribution to use for this question? Why?

b) What is the probability that 30 or more will survive for a year? Use you will need to use the appropriate command in R of d, p, q, or r and use the appropriate values as arguments.

Hint: Remember that when the question is a >= probability, this is equivalent to saying what is 1-probability of less than surviving.

Answer 1

Answer)

If we have only two possible outcomes that is either a success or failure, and fixed number of trials then we can use binomial distribution

A)

As here we have fixed number of trials 43

Probability of success = 0.65

Probability of failure = 0.35

So, we will use binomial distribution

B)

We need to find

P(30 or more)

P(30) + P(31)...+p(42) + p(43)

Here we need to use the binomial formula

P(r) = ncr*(p^r)*(1-p)^n-r

Ncr = n!/(r!*(n-r)!)

N! = N*n-1*n-2*n-3*n-4*n-5........till 1

For example 5! = 5*4*3*2*1

Special case is 0! = 1

P = probability of single trial = 0.65

N = number of trials = 43

R = desired success = at least 30

After substitution

Required probability is =  0.31472825364