Final answer:
The questions provided pertain to using different probability distributions such as binomial, normal, and exponential to answer real-world statistical problems in the field of Mathematics at the College level.
Step-by-step explanation:
The subject of these questions is Mathematics, specifically focusing on statistics and probability concepts applied to real-world situations. Various distributions such as binomial distribution in hypothesis testing, exponential distribution for the time between events, and normal distribution for sample means are utilized to answer these questions.
In the scenarios provided, probabilities are calculated based on given sample sizes and sample statistics, such as the percentage of satisfied customers or the mean amount of money spent at a supermarket.
For example, in the first scenario, a hypothesis test could be performed using a binomial distribution if the sample size is large enough, and the conditions for a normal approximation are met. The student would use the normal distribution to test if the actual proportion of customers preferring Brand A is different from the expected 42 percent.
Regarding the amount of time customers arrive after the previous one (part e), if the times are independent and the rate at which customers arrive is constant, then it would be reasonable to say that an exponential distribution applies to the situation.