Final answer:
The initial request doesn't align with the intermediate value theorem, which is not applicable to the linear function provided. Other parts of the text seem unrelated and pertain to statistics and calculus, but without a specific context or distribution table, it is not possible to provide an accurate answer to the calculations requested.
Step-by-step explanation:
The student has multiple elements scattered throughout the provided text which could lead to confusion. The initial request to use the intermediate value theorem to approximate a zero for the function f(x) = 8x is not well-suited since the intermediate value theorem cannot be applied to this linear function directly to find zeros. However, the zero of the function f(x) = 8x can be found simply by setting f(x) equal to zero and solving for x, yielding x = 0.
Other parts of the question pertain to different concepts such as probability distributions, z-scores, percent defective cars, assumptions in calculations, and properties of a function within a certain interval. These elements suggest a blend of statistics and calculus concepts.
Without a specific distribution table or context, we cannot calculate P(x = 3), P(1 < x < 4), or P(x ≥ 8). However, some parts of the text reference the normal distribution with a mean (µ) and standard deviation (σ), including the empirical rule percentages for z-scores of ±1, ±2, and ±3 around the mean.