Question

a survey was given to randomly selected residents of a state. they were each asked whether they approved of a new sports stadium being built and where it should be built. the results of the survey are shown in the table below. using the data in the table, the team makes conclusions by calculating probabilities related to a randomly selected resident from the survey. which conclusion can be made from the data? a. given the stadium should be built, it should be built downtown. b. given a suburban location, the stadium should not be built. c. given the stadium should be built, it should be built in the suburbs. d. given a downtown location, the stadium should not be built.

Explanation:

Step1: Calculate probability of building downtown given approval

The number of people who approve and want it downtown is 98, and the total number of people who approve is 263. The probability $P(\text{downtown}|\text{approve})=\frac{98}{263}\approx0.373$.

Step2: Calculate probability of building in suburbs given approval

The number of people who approve and want it in suburbs is 126, and the total number of people who approve is 263. The probability $P(\text{suburbs}|\text{approve})=\frac{126}{263}\approx0.479$.

Step3: Calculate probability of building in rural given approval

The number of people who approve and want it rural is 39, and the total number of people who approve is 263. The probability $P(\text{rural}|\text{approve})=\frac{39}{263}\approx0.148$.

Step4: Analyze options

Since $P(\text{suburbs}|\text{approve})$ is the highest among the three - location probabilities given approval, if the stadium should be built, it is most likely to be built in the suburbs.

Answer:

C. Given the stadium should be built, it should be built in the suburbs