Question

select the correct answer.
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.

	location
build stadium	downtown	suburbs	rural	total
yes	98	126	39	263
no	102	74	171	347
total	200	200	200	600

which conclusion can be made from the data?
a. given the stadium should be built, it should be built downtown.
b. given a downtown location, the stadium should not be built.
c. given a suburban location, the stadium should not be built.
d. given the stadium should be built, it should be built in the suburbs.

Explanation:

Step1: Calculate P(Downtown|Yes)

$\frac{98}{263} \approx 0.373$

Step2: Calculate P(Suburbs|Yes)

$\frac{126}{263} \approx 0.479$

Step3: Calculate P(Rural|Yes)

$\frac{39}{263} \approx 0.148$

Step4: Calculate P(No|Downtown)

$\frac{102}{200} = 0.51$

Step5: Calculate P(No|Suburbs)

$\frac{74}{200} = 0.37$

Answer:

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