Question:
A researcher samples n individuals randomly from a population of blackbuck and identifies their sex. The number of females in the sample follows
- An exponential distribution
- A binomial distribution
- A Poisson distribution
- A normal distribution
Rephrasing the Question:
What is the probability distribution of the sex of individuals in a population?
Answer:
Binomial distribution (option 2).
Explanation:
Since sex (in this simple example) can only be binary – that is, there is only the option of being male or female – the answer is the one that allows for two discrete possibilities. This is the binomial distribution.
This is all you need to answer the question, but let’s take this opportunity to go over the binomial distribution a little.
Binomial distribution is a probability distribution that we use to work with the probability of obtaining one of two outcomes. It is applied when each trial has the same chance of attaining a specific result. In our question, the probability of an individual blackbuck being female is the same for each animal, independent of the others.
Suppose we wanted to know what the probability of there being exactly 15 females in a population of 50 blackbucks, if the probability of an individual animal being female is 50%. We can calculate this using the equation for binomial distribution.
If we calculate this, along with the probabilities of there being exactly 0 females, exactly 1 female, exactly 2 females, etc., up to exactly 50 females, we get a graph like this:
Sources:
https://www.youtube.com/watch?v=WR0nMTr6uOo
An excellent video about the binomial distribution – you don’t need all the details for the NET exam, but this is good resource if you’re trying to understand where and how it’s applied
https://www.radford.edu/~scorwin/courses/200/book/150BinomialDistribution.html