Question

3. 4.16/8.33 points Previous Answers My Notes O Ask Your Teacher BBBasicStat8Acc 6.1.011. nhe erine shePner for whemat lea, 70% the tems purchased were on sale or purchased with a coupon. In the following table, income units are in thousands 8 hene e8 iteet 5-1 Income range 15-25 25-35 35-45 45-5S 55 ar more 40 Midpoint x | Percent of super shoppers 21% a) Using the income midaintsx and he perE 20 30 22 % 50 60 14% 16% 19% 8% No. The events are indistirict and the probabilities sum to Rs do ve have e velid prabebility distribution? Explein. Yes. The events are distinct and the prababilities sum to 1. of supe Yes. The events are distinct and the probabilities do not sum to 1. Yes. The events are indistinct and the probabilities sum to less than 1. No. The events are indistinct and the probabilities sum to more than 1. (b) Use a histaaram ta oraph the prabability distribution of part (a). (Select the correct graph.) (c) Camoute the expected income of a super shopper (in thausands of dallars). (Enter a number. Round yaur answer to two decimal places.) thousends of dllars (d) Comoute the standard deviation o for the income of super shoppers thousands dollars). (Enter a number. Round your answer to two decimal places.) thousands of dollars

What is the income distribution of super shoppers? A supermarket super shopper is defined as a shopper for whom at least 70% of the items purchased were on sale or purchased with a coupon. In the following table, income units are in thousands of dollars, and each interval goes up to but does not include the given high value. The midpoints are given to the nearest thousand dollars. Income range 5-15 15-25 25-35 35-45 45-55 55 or more Midpoint x 10 20 30 40 50 60 Percent of super shoppers 21% 14% 22% 16% 19% 8%

(a) Using the income midpoints x and the percent of super shoppers, do we have a valid probability distribution? Explain.

(b) Use a histogram to graph the probability distribution of part (a). (Select the correct graph.)

(c) Compute the expected income μ of a super shopper (in thousands of dollars). (Enter a number. Round your answer to two decimal places.)
μ =   thousands of dollars

(d) Compute the standard deviation σ for the income of super shoppers (in thousands of dollars). (Enter a number. Round your answer to two decimal places.)
σ =   thousands of dollars

Answer 1

Colation: What as the income distribution of super Shoppers is Required information is given by Irconde monge 5-15 15-05 mid point x 10 20 percent of Cuper Ort. 101. 59.5 30 00:1 85-105 40 16.1. 405-55 Sore 50 60 19.1. 8.1. = Shoppers Calculate ③ using the income mid points x and percenti we have to obtained the income mid points x and the percent of Guper (shoppers is) Gere, Sums shoppers = to.21+ 0.14+ 0.00+ 0.16+0.19 +0.8] -140 herefore, Yes, The events are distinct and the probabilite's sum to di Option @ is correct answer o cuse a bitstograph to graphi- to histogram by using gilla we have to obtained data is

Income 5-15 15 05 05-05 (95-415 45-55 ss more Ronge ao 20 30 10 40 410 50 60 50 Hiltogram Giner shoppi 0 10 20 30 40 Income 50 60 > Therefore, option is correct answer. © Compute the expected in Comer- con have to obtained the expected in come le of a Super Shopper is, fere, Expected income ins. I= I x x PCXD

ei= (lox 0.21] + DOVO.K(1) 46130 X 0.00] + C40*0.16] +C50* O'LQI-+C600.08) Lºt - (+ 28-6.64 6. | 4 q5 + C: B] 21 - 09. 2) Therefore, Expected in come 101= 62.2 is thousand dollars. Compute standard deviation i lale have to obtained the standard of Super (shoppers is deviation of the income (fere, Standard deviation is, -=fE CU 2 - Etuj] I where Econ=lt102*0-01]+[207*0.143+ [302* 0.90] + [C102*0.16) +(502x0.La]+[602*0.08] ] ET 4+ 56+2987056 +4+5+988] (E Cu?)= W9u

Golwau -69.1)2 -/1994 - 1036.84 V@5+:16 = 16:00 C (16 thousand dollars. Therefore, Standard deviation is = 1161 thousand dollars