Final answer:
The student's question is about the probability distribution for cheesecake sales at a local bakery, which quantifies the likelihood of various sales outcomes and assists in planning and decision-making.
Step-by-step explanation:
The question pertains to a probability distribution for a local bakery's cheesecake sales. A probability distribution provides a way to quantify the likelihood of different outcomes for a random variable, which in this case represents the number of cheesecakes sold in a day.
To define the random variable X, we would state it as 'the number of cheesecakes sold per day.'
If we had the actual distribution, we could state the type of distribution it is (for example, binomial, Poisson, normal, etc.), and use it to calculate probabilities of interest, such as the probability of selling more than a certain number of cheesecakes on a given day.
Moreover, knowing the average (or mean) sales and possibly other parameters like the standard deviation, we could provide insightful probabilities and expectations for bakery planning and inventory management.
For the baker's case in the question, they would use the established probability distribution to make data-driven decisions on how many cheesecakes to prepare in order to meet demand without overproducing.
The probability distribution could also be used to answer questions similar to those in the sample you provided, such as 'What is the probability that the baker will sell exactly one batch?' or 'On average, how many batches should the baker make?'