Question

one hundred six people who grew up in either city a or city b were surveyed to determine whether they preferred country music or blues (both and neither were not acceptable responses). of those who grew up in city b, 43 preferred blues and 19 preferred country music. of those who grew up in city a 23 preferred country. answer parts (a) through (d) below. a. complete the two - way table summarizing the reviews.

	country music	blues
city b	blank	43

(type whole numbers.) b. make a venn diagram from the table in part (a). choose the correct answer below. a. venn - diagram option a b. venn - diagram option b c. venn - diagram option c d. venn - diagram option d c. how many city b residents preferred country? blank (type a whole number.) d. how many respondents preferred country? blank

Explanation:

Step1: Find number of City A residents who prefer blues

The total number of people surveyed is 106. The number of City B residents is \(43 + 19=62\). So the number of City A residents is \(106 - 62 = 44\). Since 23 City A residents prefer country music, the number of City A residents who prefer blues is \(44 - 23=21\).

Step2: Complete the two - way table

The number of City B residents who prefer country music is 19.

Step3: Analyze Venn - diagram

The Venn - diagram should have two overlapping circles, one for City B and one for Country music. The number of City B residents who prefer blues is 43, the number of City B residents who prefer country music is 19, and the number of non - City B (City A) residents who prefer country music is 23, and the number of City A residents who prefer blues is 21. The correct Venn - diagram is the one where the intersection of City B and Country music has 19, City B non - intersecting part has 43, Country music non - intersecting part has 23 and the part outside both but within the total set has 21.

Step4: Answer part c

The number of City B residents who preferred country is 19.

Step5: Answer part d

The number of respondents who preferred country is \(23+19 = 42\).

Answer:

a.

	Country Music	Blues
City B	19	43

b. (The correct Venn - diagram depends on the actual options' details, but based on the above analysis, the one with 19 in the intersection of City B and Country music, 43 in City B non - intersecting part, 23 in Country music non - intersecting part and 21 outside both)
c. 19
d. 42