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

Answer:

p (X= 4) = 0.266

Explanation:

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

As per binomial setting

p (X= k)  = $\frac{n!}{k! * (n-k)!} p^k(1-p)^{n-k}$

Substituting the given values, we get -

p (X= 4)  = $\frac{8!}{4! * (8-4)!} 0.46^4(1-0.46)^{8-4}$

p (X= 4)   =   $\frac{8*7*6*5 *0.44775 * 0.0850306}{4*3*2*1}$

p (X= 4) = 0.266