In probability problems we typically assume a model for a random (uncertain) process and evaluate probabilities of potential outcomes or events — what might the data look like? For example
- If human body temperatures (\(^\circ\) F) have a Normal distribution with mean 98.6 and SD 0.8, what is the probability that the mean body temperature of a random sample of 100 people is less than 98.3?
- If 10% of Cal Poly students are left-handed, what is the probability that in a class of 35 students at least 5 are left-handed?
In problems involving statistical inference we observe sample data and make conclusions about the process that generated the data. For example
- The mean body temperature for a random sample of 100 healthy people is 98.3\(^\circ\) F. Is there evidence that mean healthy human body temperature is less than 98.6\(^\circ\)?
- In a class of 35 Cal Poly students 5 are left-handed. Estimate the proportion of Cal Poly students in general that are left-handed.
There is a close relationship between probability and statistics. In this chapter, we’ll investigate some applications of probability in statistical contexts.