Question

Biologists estimate that a randomly selected baby elk has a 46% chance of surviving to

adulthood. Assume this estimate is correct. Suppose researchers choose 8 baby elk at
random to monitor. Let x = the number that survive to adulthood.
Determine whether the scenario above describes a binomial setting. Justify your answer.
Use the binomial probability formula to find P (X = 4). Interpret this value.

Answer 1

p (X= 4) = 0.266

Step-by-step explanation:

Probability of randomly selected baby elk to survive adulthood = 46%

As per binomial setting

p (X= k) =
`(n!)/(k! * (n-k)!) p^k(1-p)^(n-k)`

Substituting the given values, we get -

p (X= 4) =
`(8!)/(4! * (8-4)!) 0.46^4(1-0.46)^(8-4)`

p (X= 4) =
`(8*7*6*5 *0.44775 * 0.0850306)/(4*3*2*1)`

p (X= 4) = 0.266