CChegg Study I Guided S xMM Mathway Math problem you select a random san X Round

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CChegg Study I Guided S xMM Mathway Math problem you select a random san X Rounding Numbers Calou X P Take a Test Gabrielle Bur X C A https:// www.mathxl.com /Student/PlayerTe stId 46586 aspx Apps UF U UF U D STARS C iversity of Florida UF Reg versity of Florida: versity of Florida ollege Por Agenda Creator I Ev MyMathLab Gabrielle Burch 1/15/16 9:28 PM Test: Chapter 7 Post-Test Time Remaining: 01:18:49 Submit Test This Question: 7 pts 3 of 5 (2 complete This Test: 18 pts possible Question Help HCH A survey indicates that 37% of consumers from a certain region are willing to spend extra for products and services from socially responsible companies. The researchers define these consumers as socially conscious consumers. According to one of the researchers marketers need to know who these consumers are if they want to maximize the social and business return of their cause-marketing efforts. Suppose a sample of 100 consumers from the region is selected. If possible, use the normal distribution to approximate the sampling distribution of the proportion. Complete p (a) through (g) below a. What is the probability that in the sample fewer than 37% are willing to spend extra for products and services from socially responsible companies? The probability is (Round to two decimal places as needed.) b. What is the probability that in the sample between 31% and 43% are willing to spend extra for products and services from socially responsible companies? The probability is (Round to two decimal places as needed.) c. What is the probability that in the sample more than 31% are willing to spend extra for products and services from socially responsible companies? The probability is (Round to two decimal places as needed.) d. If a sample of 400 is taken, what is the probability that in the sample fewer than 37% are willing to spend extra for products and services from socially responsible companies? The probability is 1% (Round to two decimal places as needed.) e. If a sample of 400 is taken, what is the probability that in the sample between 31% and 43% are willing to spend extra for products and services from socially responsible companies? The probability is 1% (Round to two decimal places as needed.) f. If a sample of 400 is taken, what is the probability that in the sample more than 31% are willing to spend extra for products and services from socially responsible companies? Enter your answe n each of the answer boxes 10:28 PM 1/15/2016

Explanation / Answer

Std deviation = (pq/n) = (0.37 × 0.43/100) = 0.040

a.) Probability = P( X < 0.37)

= P ( Z < (0.37 - 0.37)/(0.37× 0.63/100))

= P( Z <0) = 0.5

B.) P(0.31 < X < 0.43)

= P ( (0.31 - 0.37)/0.040 < Z < (0.43 - 0.37)/0.040)

= P ( -1.504 < Z < 1.504)

= 0.9337 - 0.0663

= 0.8674

c.) P(X > 0.31)

= P(Z > (0.31-0.37)/0.04)

= P(Z > -1.5042)

= 0.9382

d.) P(X<0.37)

= P(Z < (0.37-0.37)/(0.37×0.43/400)

= P(Z < 0) = 0.5

For a sample of size 400

Std deviation= (0.37×0.43/400) = 0.020

e.) P(0.31 < X < 0.43)

= P(-3.01 < Z < 3.01)

= 0.9987 - 0.0013

= 0.9974

f.) P(X > 0.31)

= P(Z > - 3.01)

= 0.9987

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