Final answer:
The probability questions regarding phone calls involve understanding the average call time or distribution of times, while the question regarding Jeremy and Jasmine involves plotting a budget constraint and maximizing utility based on given values.
Step-by-step explanation:
The question appears to be addressing concepts from probability and budget constraints in mathematics, specifically within the contexts of phone call durations and budgeting for communication choices. To answer the questions concisely:
a. Given an average of 20 calls during peak time, the probability of making more than 20 calls can be found using a probability distribution, likely a Poisson or binomial distribution depending on the context. However, the exact calculation requires additional context.
b. To find the probability of an individual customer's excess time being longer than 20 minutes, we must know the distribution of excess times. Without this information, we cannot compute the probability.
c. Probabilities in parts (a) and (b) are different due to the distinct situations: part (a) deals with the average of many employees, while part (b) focuses on the excess time of a single customer.
Regarding the budget constraints and utility maximization:
Jeremy has a weekly budget of $10 to spend on staying in touch with Jasmine, which he can allocate between phone minutes at five cents per minute and round trips that cost $2 each. The optimum allocation would be found by plotting and analyzing the points of Jeremy's consumption choice budget constraint and using the provided utility values to find the point at which his total utility is maximized. This involves setting up equations reflecting the budget constraint, plotting these points, and using the given utility figures to determine the best choice for Jeremy.