it came from Wholesaler B ? 5. A consumer survey randomly selects 2000 people an
ID: 2930568 • Letter: I
Question
it came from Wholesaler B ? 5. A consumer survey randomly selects 2000 people and asks them about their income and their television-watching habits. The resul numbers within the table reflect people in various categories of TV-watching and annual income. As a reward for participation, each person is given a small prize. Then the names are placed in a box and one name is randomly selected to receive the grand prize of a free vacation trip to Edgewood Its are shown in the following table. The Hours of TV Watchod per Week Annual Income 0-8 9-15 16-22 23-30 More than 30 TOTAL Less than $12,000 $ 12,000-$ 24,999 $25,000- $39,999 $ 40,000-$ 59.999 $ 60,000 or more 168 541 60 TOTAL 143 336 657 What is the probability that the winner of the grand prize: a. Earns at least $ 25,000? b. Watches TV at least 16 hours each week ? c. Earns at least S 40,000 and watches TV at least 23 hours a week? d. Earns less than $ 40,000 or watches TV at most 22 hours each week? e. Watches TV at most 22 hours each week given that he/she earns less than $ 60,000? f. Watches TV no more than 30 hours each week? g. Watches TV for at most 15 thours each week or earns at least S 25,000?Explanation / Answer
Question 5
(a) Pr(at least $ 25000) = (654 + 541 + 252)/ 2000 = 0.7235
(b) Pr(watches TV atleast 16 hours each week) = (336 + 657 + 653)/ 2000 = 0.823
(c) Pr(at least earn $ 40000 and watched TV atleast 22 hours a week)
= NUmbr of people who earn atleast $ 40000 and watch TV atleast 22 hours a week/ Total number of people
= (165 + 100 + 55 + 12)/ 2000 = 0.166
(d) Pr(at most earn $ 40000 and watch TV atmost 22 hours a week)
= NUmbr of people who earn atmost $ 40000 and watch TV atmos 22 hours a week/ Total number of people
= (11 + 15 + 8 + 10 + 19 + 28 + 18 + 32 + 88)/ 2000 = 0.1145
(e) Pr(at most watche TV 22 Hours each week l earns less than $ 60000)
= Pr(at most watches TV22 HOurs each week and earns less than $ 60000)/ Pr(Earns less than $ 60000)
= (143 + 211 + 336 - 73 - 60 - 52)/ (2000 - 252) = 0.2889
(f) Pr(Watches TV no more than 30 Hours a week) = (2000 - 653)/ 2000 = 0.6735
(g) Pr(Watches TV at most 15 hours or earns at least $ 25000)
= (143 + 211 + 168 + 385 - 11 - 15 - 10 - 19)/ 2000 = 0.426
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