Question

Biologists estimate that a randomly selected baby elk has a 44% chance of surviving to adulthood. Assume this estimate is

correct. Suppose researchers choose 7 baby elk at random to monitor.
Let X = the number that survives to adulthood.
What is P(X = 4)? Interpret this value.

Answer 1

There is a 27.42% chance that exactly 4 out of 7 randomly selected baby elk will survive to adulthood, using the binomial probability formula.

Step-by-step explanation:

The question asks for the probability that exactly 4 out of 7 randomly selected baby elk will survive to adulthood, with each having a 44% chance of survival. To calculate this, we use the binomial probability formula:

P(X = k) = C(n, k) × (p)^k × (1-p)^(n-k)

Where:

• C(n, k) is the number of combinations of n items taken k at a time.
• n is the number of trials (in this case, 7 baby elk).
• k is the number of successes (in this case, 4 survivals).
• p is the probability of success on a single trial (44% or 0.44).

Now we apply the values to the formula:

P(X = 4) = C(7, 4) × (0.44)^4 × (0.56)^3

P(X = 4) = 35 × (0.04486656) × (0.175616)

P(X = 4) = 0.2742

The interpretation of this value is that there is a 27.42% chance that, in a group of 7 randomly selected baby elk, exactly 4 will survive to adulthood.