Final answer:
The student's question involves calculations related to normal distribution, the central limit theorem, probability density function for investments, and the use of normal distribution tables and technology in statistics.
Step-by-step explanation:
The question asks about the rate of return for an investment, which can be described by a normal distribution with a mean of 33. The information provided suggests that a sample is being drawn from this normally distributed population, and the context presents a scenario relating to investment decisions based on probabilities and expected returns. Additionally, there is mention of the central limit theorem, which states that the distribution of sample means will tend to be normally distributed regardless of the underlying population distribution, given a sufficiently large sample size. This principle is essential for making statistical inferences about populations based on sample data. The student is also introduced to aspects of probability distributions, such as the probability density function (PDF), the empirical rule, and the use of standard normal distribution tables or technology to find probabilities and percentiles.