Answer:
Explanation:
The <em>probability mass function</em> (<em>PMF</em>), or <em>frequency function</em>, is the function that gives the probabilities that a <em>discrete random variable</em> take some values.
In this problem, it is requested the frequency function (PMF) for the <em>number of purchasers, among the next 15, who select a chain-driven model</em>.
Then , you need to find, the function that gives P(X=0), P(X=1), P(X=2), P(X=3), . . . up to P(X=15).
Such as any function, the frequency function can be presented as a formula, as a table, or as a graph.
Note that the statement represents a binomial disbribution in which success is that a customer select a chain-driven model and the fail is that a cusotmer does not select a chain-driven model.
The binomial probability for X = the number among the 15 purchasers who select the chain-driven model is given by the formula:
Where:
- n is the number of times the experiment is performed: 15 in our problem
- p is the probability of succes: 0.75 in our problem
- 1-p is the probability of fail: 0.25 in our problem
Then, substitute:
That is the frequency function.
If you want to give it as a table you must find P(X=1), P(X=2), P(X=3), . . . up to P(X=15) using that function. That is not part of the question.