Based on the number of customers from last week, the fraction is closest to the probability that the next customer will pay with cash is 54/249
Suppose population is wide and you cannot evaluate all the population at once. Then you do sampling of large enough size randomly. The mean of that sample will be then the estimate for the mean that population will pertain.
Experimental probability calculates the probability of some event from the results of experiments.
For an event E, we get the experimental probability of that event
where, is denoting experimental probability of occurrence of E.
Here, the customers are not all known to us, they are population.
But we have some data of the previous customer. Taking them as the sample, we have:
Experimental probability of an event from sample = Predicted probability for that event in population.
For this case, from the previous data, we have:
Total customers who paid = 153 + 42 + 54 = 249
Total customers who paid with cash = 54
Thus, if we take:
E = event that a customer pays with cash, then:
This is the probability deduced from the previous data that the next customer will pay with cash.
Thus, based on the number of customers from last week, the fraction is closest to the probability that the next customer will pay with cash is 54/249
Learn more about probability here:
3 points define a parabola, so the regression will be unique. You want to find a quadratic polynomial such that
where the system above is generated by setting , , and .
Since , we have
So the regression for the given data points is .