Question

Let's eat: A fast-food restaurant chain has 584 outlets in the United States. The following table categorizes them by city population size and location, and presents the number of restaurants in each category. A restaurant is to be chosen at random from the 584 to test market a new menu. Round your answers to four decimal places. Population of City Region NE SE SW NW 25 32 11 7 Under 50,000 50,000 - 500,000 56 91 69 28 Over 500,000 145 26 31 63 Send data to Excel (a) Given that the restaurant is located in a city with a population over 500,000, what is the probability that it is in the Northeast? (b) Given that the restaurant is located in the Southeast, what is the probability that it is in a city with a population under 50,000? (c) Given that the restaurant is located in the Southwest, what is the probability that it is in a city with a population of 500,000 or less? (d) Given that the restaurant is located in a city with a population of 500,000 or less, what is the probability that it is in the Southwest? (e) Given that the restaurant is located in the South (either SE or SW), what is the probability that it is in a city with a population of 50,000 or more?

Answer 1

Here we have,

Population of city	Region
	NE	SE	SW	NW	Total
Under 50000	25	32	11	7	75
50000-500000	56	91	69	28	244
over 500000	145	26	31	63	265
Total	226	149	111	98	584

a) P(Northeast I over 500,000) PCNE and over 500 000) r 500,000) . 145/584 145 = 21 265/584 = 265 5 = 0.54717 -0.5472 b) PCunder 50000 SE) = P(under 50000 and SE) P(SE) 32/584 - telo 149/54 = 0.21476 = 0,2148 c) P( 500,000 or less sat - P(pop. 500,000 or less and sw) P(sw) P (Pop under 50000 and sw) + P ( Pop 50000 - 500000 and Sw P(sw) 11/584 + 69/584 11789 - 90 1584 = 0.7207

d) PCsw I pop 50.000 or less) Prow and pop" 5000 oo ay less) PC popa 500000 or less) p(sw and popa under 50000) +P(sw ond pop'500 60.000) A Coop soooo) +P (Pop" (50000-500000)) 11/584 + 69/586 80 = 319 75/584+246/584 = 0.2508 e) PC popa of 50000 or more south) I PC popa under 50000 / south) ci - P (popp under 50000 low or SE) PE P(pop" under 50000 and sw) +P (popa under 50000 and SE) plow) + P(SE) 1/585 + 32/584. 111/584 + 149/584 43 217 2.60 260 = 0.8346