Final answer:
To find the probability that in a random sample of 163 people from a town with 71.1% college students, more than 50 are not college students, one needs to use the binomial distribution formula or a normal approximation, and calculate P(X > 50) using statistical software or a calculator.
Step-by-step explanation:
The subject of this question is Mathematics and it concerns the concept of probability distributions, specifically the binomial distribution. Given that 71.1% of a town's population consists of college students, we need to find the probability that more than 50 out of a sample of 163 people are not college students. We can use the binomial distribution formula to solve this, or a normal approximation if the sample size is large enough.
First, we identify the probability 'p' of a person not being a college student, which is 1 - 0.711 = 0.289. Next, we define the number 'n' of trials, which is the sample size 163, and the number 'x' of successes, in this case, the number of people who are not college students which should exceed 50.
To find the probability that more than 50 people are not college students, we calculate P(X > 50). This can be done using cumulative distribution functions (CDFs) of binomial or normal distributions, depending on whether the binomial conditions are met or if a normal approximation is more appropriate due to a large sample size. The calculation may require software or a calculator that can handle statistical functions.