Question

Age	Gender	Children	Household Income ($)	Total non RE Investments	Financial transactions	Potential RE investment?	Electric car
38	Female	Yes	75200	12200	4	No	No
30	Male	Yes	70300	12400	4	No	No
41	Female	No	48200	26800	5	No	No
28	Female	No	95300	19600	6	Yes	No
31	Female	Yes	73300	15100	5	Yes	No
32	Male	Yes	123400	39700	3	No	No
32	Male	Yes	73900	21900	2	Yes	No
26	Female	Yes	54300	41900	2	Yes	No
26	Male	No	93100	16100	4	Yes	No
34	Female	No	60100	18400	11	Yes	No
33	Female	No	48600	33800	3	No	No
35	Female	No	43500	15500	6	Yes	No
28	Female	Yes	73600	17300	7	No	No
30	Male	Yes	68200	47900	5	No	No
30	Female	Yes	61900	28200	3	No	No
30	Male	No	57600	19400	6	Yes	No
33	Male	No	82300	31000	12	Yes	No
28	Male	Yes	64600	21300	6	No	No
27	Female	Yes	61100	21300	10	No	No
23	Female	Yes	31200	21300	7	No	No
30	Female	No	92600	34100	6	No	No
28	Male	No	68300	32600	7	No	No
41	Male	No	35100	0	10	Yes	No
29	Male	No	85700	20800	10	Yes	No
33	Female	Yes	140300	23100	6	Yes	No
30	Male	Yes	108200	39800	9	No	No
29	Female	No	61100	17900	2	No	No
33	Male	Yes	33900	33300	2	No	No
30	Female	Yes	54400	21800	8	Yes	No
30	Male	No	61200	54000	7	No	No
36	Female	Yes	58000	34800	12	Yes	No
33	Female	Yes	90700	36100	7	Yes	Yes
28	Female	No	95200	44300	5	Yes	Yes
28	Male	Yes	50500	21400	5	No	No
28	Male	Yes	33800	8600	6	Yes	Yes
35	Male	No	147400	23200	3	No	No
31	Male	Yes	92600	24800	4	No	No
33	Female	No	66200	26600	5	No	Yes
32	Male	No	45700	33100	8	No	No
28	Male	Yes	60500	27000	4	No	No
27	Male	No	110600	48700	6	No	No
30	Female	Yes	60300	17100	4	Yes	No
29	Male	No	75700	19900	6	No	No
28	Male	Yes	70100	13200	9	No	No
29	Female	Yes	42100	32400	6	Yes	No
32	Female	Yes	41700	14200	5	No	Yes
33	Male	No	96900	20100	5	No	No
23	Male	No	65700	32000	5	Yes	Yes
29	Female	No	50200	41900	3	No	No
31	Male	No	61700	12000	3	No	No
33	Female	Yes	44500	14000	6	No	No
37	Female	No	51900	10000	4	No	Yes
28	Female	Yes	119100	27200	5	No	Yes
27	Female	No	49200	34500	4	Yes	Yes
33	Female	Yes	39000	26000	6	No	Yes
31	Female	No	35000	53400	3	No	Yes
30	Male	Yes	104700	23100	7	No	Yes
23	Male	No	49300	24900	5	No	No
33	Male	No	74000	10900	10	No	Yes
31	Female	Yes	57100	52500	2	No	Yes
24	Female	Yes	51400	24600	16	No	Yes
35	Female	Yes	62100	28800	6	No	No
36	Female	Yes	103000	37300	11	Yes	Yes
24	Male	No	97900	21100	9	Yes	Yes
25	Male	No	123100	40900	3	No	No
26	Female	No	322500	24700	7	No	Yes
31	Male	Yes	54800	33600	8	No	Yes
26	Male	Yes	66500	20000	6	Yes	No
26	Male	Yes	33700	23900	2	No	No
28	Male	Yes	73600	11700	8	Yes	No
26	Female	Yes	71300	19200	5	No	Yes
34	Male	No	74200	11900	6	No	No
32	Male	Yes	70000	17700	8	No	Yes
30	Male	No	40800	23900	6	No	Yes
29	Female	Yes	72500	27500	4	Yes	Yes
23	Male	No	53300	25300	4	Yes	No
28	Female	No	45600	66900	5	No	No
25	Male	Yes	73900	18800	5	No	Yes
35	Male	No	83600	24400	3	No	Yes
31	Male	No	124700	45500	9	No	Yes
35	Male	No	101600	54700	3	Yes	Yes
32	Female	Yes	205900	32200	4	No	No
29	Male	No	69700	16200	3	No	Yes
34	Female	No	95700	16000	9	No	No
30	Female	Yes	46100	24000	3	Yes	No
29	Male	No	118600	28800	3	No	Yes
42	Male	No	65400	14100	5	No	Yes
37	Female	Yes	149300	17700	11	Yes	Yes
32	Male	No	125000	29800	7	No	Yes
33	Female	No	39800	27200	3	Yes	Yes
36	Male	Yes	83500	43000	2	Yes	No
32	Female	Yes	38700	15500	7	Yes	Yes
35	Male	No	102400	8700	6	Yes	No
20	Male	No	57700	13900	14	No	Yes
30	Male	No	16200	14200	6	No	Yes
31	Female	No	43100	27100	3	Yes	No
28	Male	No	43700	22300	3	Yes	No
24	Female	Yes	39600	29500	4	Yes	Yes
30	Male	No	127500	18800	2	No	Yes
23	Female	No	33500	26400	9	Yes	Yes
29	Male	Yes	48100	16400	5	Yes	Yes
33	Male	No	52800	39500	3	No	Yes
24	Male	No	54800	20900	6	Yes	Yes
25	Female	No	46500	52800	5	No	Yes
38	Male	No	60400	36500	4	No	Yes
22	Female	Yes	202400	30400	11	No	Yes
32	Female	No	71300	39800	7	No	No
28	Female	No	62800	18100	9	Yes	No
32	Male	Yes	43900	69500	7	Yes	No
33	Female	Yes	52200	33000	5	No	Yes
32	Female	Yes	64400	32100	3	Yes	No
24	Male	Yes	77400	15200	8	Yes	No
23	Female	No	65900	49800	3	Yes	Yes
23	Male	Yes	54100	28100	6	No	No
38	Male	Yes	77400	15200	6	No	Yes
29	Male	Yes	85900	30800	3	No	Yes
28	Male	No	148600	21200	3	No	No
29	Male	No	82100	24600	4	No	Yes
36	Male	Yes	64400	24700	9	Yes	Yes
35	Female	No	86200	26300	16	Yes	No
34	Female	Yes	177100	32200	6	Yes	No
23	Male	No	68300	20300	6	No	Yes
31	Female	Yes	67900	60900	6	No	Yes
28	Male	Yes	57300	15800	11	No	Yes
33	Female	No	83600	31700	6	No	Yes
31	Male	No	77500	0	5	Yes	Yes
26	Female	Yes	61700	20900	9	Yes	Yes
38	Female	Yes	85600	37900	12	No	No
28	Male	Yes	59900	22400	7	Yes	Yes
27	Male	No	43100	26600	5	No	Yes
31	Male	No	65700	20800	10	Yes	No
34	Male	Yes	80500	31100	7	No	Yes
29	Male	Yes	88400	31200	5	No	Yes
27	Male	No	40200	0	2	No	No
26	Male	Yes	84000	38900	7	Yes	Yes
33	Male	Yes	34400	29500	4	Yes	Yes
33	Male	Yes	55800	16100	5	No	No
34	Male	Yes	64900	15800	7	No	Yes
31	Male	Yes	41100	27500	4	No	Yes
37	Female	Yes	39100	13000	7	No	No
27	Male	No	58200	68100	5	Yes	No
32	Male	Yes	46500	18500	7	Yes	Yes
25	Female	Yes	45100	27100	2	No	Yes
31	Female	Yes	69900	25900	5	No	Yes
38	Male	No	63700	18400	2	No	No
31	Female	No	40500	59200	4	No	Yes
28	Female	Yes	62600	67900	5	No	No
29	Female	Yes	73400	36700	7	No	Yes
34	Female	No	35000	32400	9	No	Yes
35	Female	No	114000	10300	4	Yes	Yes
30	Male	No	70800	39300	7	No	Yes
32	Female	Yes	60300	13800	6	No	Yes
31	Male	No	78700	11100	4	No	Yes
29	Female	No	179700	28600	2	No	No
31	Male	Yes	157200	22100	6	No	Yes
31	Female	No	67300	16700	6	No	Yes
22	Female	No	49800	19400	6	Yes	Yes
19	Male	Yes	43400	54600	4	Yes	Yes
31	Female	Yes	71100	41500	2	Yes	Yes
22	Female	Yes	42100	23300	9	No	No
26	Male	Yes	42200	29700	8	No	Yes
34	Male	No	63300	33200	2	Yes	Yes
37	Male	No	55700	56300	5	Yes	No
36	Female	No	107900	25900	5	No	Yes
27	Female	Yes	44800	63500	6	Yes	Yes
32	Male	No	94700	18700	7	Yes	Yes
27	Female	No	112700	49700	4	No	Yes
32	Male	Yes	114900	15000	5	Yes	Yes
24	Female	Yes	112700	8200	7	Yes	No
38	Female	No	60900	36300	9	Yes	No
33	Female	No	137800	50200	7	No	Yes
19	Male	Yes	47200	13500	10	No	Yes
33	Male	Yes	70900	37500	4	Yes	Yes
25	Female	No	52000	26800	7	No	No
27	Male	Yes	166500	30300	5	No	No
35	Female	No	88000	46300	18	No	Yes
29	Male	No	41800	14400	9	Yes	Yes
31	Male	No	60300	0	4	Yes	Yes
29	Female	Yes	53400	18800	5	Yes	Yes
31	Female	Yes	46700	40900	5	No	Yes
32	Male	Yes	59600	23300	7	Yes	No
22	Female	Yes	27700	11900	4	No	No
29	Male	Yes	48900	28100	10	Yes	Yes
28	Female	No	56600	20400	8	No	Yes
26	Male	No	32500	14900	7	No	No
33	Female	Yes	74500	33900	3	No	No
35	Male	No	69800	15100	6	No	No
27	Male	Yes	48100	133400	5	No	No
33	Female	Yes	95900	18300	7	Yes	Yes
30	Female	No	76500	28700	10	Yes	Yes
28	Male	No	43700	50900	6	Yes	Yes
35	Female	Yes	72700	25600	4	No	Yes
34	Female	No	140100	30700	0	Yes	Yes
28	Male	No	76600	64300	5	Yes	Yes
30	Male	Yes	65300	67200	7	Yes	Yes
37	Male	Yes	161100	62200	11	No	Yes
32	Male	No	64900	33100	12	No	No
21	Male	Yes	59800	26000	4	No	No
31	Female	Yes	87900	18400	5	Yes	Yes
31	Male	Yes	174900	53000	12	Yes	Yes
23	Male	Yes	40700	46300	3	No	No
34	Male	Yes	36700	32700	5	Yes	Yes
31	Male	No	167800	50900	4	No	Yes
28	Female	No	168500	19200	2	No	No
30	Male	Yes	112100	18300	3	Yes	No
25	Male	No	65500	17800	2	No	No
32	Female	No	73500	41800	6	Yes	No
30	Male	Yes	59100	7100	7	Yes	No
28	Male	No	73900	15500	8	Yes	No
33	Male	Yes	120800	22900	4	No	No
34	Female	Yes	25100	10000	4	Yes	No
34	Female	Yes	137900	53300	6	No	No
33	Female	Yes	70200	32400	7	Yes	No
26	Male	No	90900	85600	2	No	No
28	Female	No	65500	26400	6	Yes	No
23	Male	No	86200	30400	5	Yes	No
31	Male	No	45900	24000	8	Yes	No
28	Female	No	76000	17500	0	No	No
29	Male	Yes	82700	11000	5	No	No
30	Female	Yes	57400	9400	5	No	No
30	Male	No	53700	34700	12	No	No
31	Female	Yes	29900	44200	3	Yes	No
22	Male	Yes	94800	20700	5	No	No
34	Male	Yes	67300	29000	3	No	No
30	Female	Yes	41200	29800	3	No	No
34	Female	Yes	70400	95200	21	Yes	No
25	Male	Yes	120600	21500	5	Yes	No
32	Female	No	63900	23100	4	No	No
31	Female	Yes	98800	13900	5	Yes	No
29	Female	Yes	53300	28900	7	No	No
28	Female	Yes	30000	70400	8	No	No
26	Female	Yes	93200	12400	4	No	No
26	Male	No	84100	27800	9	Yes	No
26	Female	Yes	124000	19900	5	No	No
29	Female	Yes	73400	28000	7	No	No
32	Female	No	45500	75000	6	Yes	No
37	Female	Yes	88400	14000	9	No	No
32	Male	No	74900	20900	4	No	No
33	Female	Yes	51700	47200	6	No	No
36	Female	Yes	78700	57200	5	No	No
30	Male	Yes	30700	42900	7	Yes	No
31	Male	Yes	56000	44200	1	Yes	No
28	Female	Yes	88400	28000	4	Yes	No
25	Male	Yes	201700	24500	6	Yes	No
29	Male	Yes	71600	18100	9	No	No
31	Female	Yes	59000	20900	7	No	No
32	Male	Yes	57300	32100	6	No	No
32	Male	Yes	91900	44500	6	Yes	No
38	Male	Yes	68300	20100	4	Yes	No
35	Male	No	93900	36000	8	Yes	No
34	Male	No	61200	12600	12	No	No
33	Male	Yes	128800	19300	6	Yes	No
32	Female	No	77900	33300	13	Yes	No
26	Female	Yes	67700	23600	2	No	No
23	Female	Yes	63300	49400	7	No	No
32	Male	No	55000	23700	1	No	No
25	Female	Yes	100700	35700	4	Yes	No
27	Male	Yes	148000	19900	10	Yes	No
22	Male	No	59600	30600	9	No	No
33	Female	No	51600	24600	2	No	No
33	Male	No	48400	18000	1	Yes	No
29	Male	Yes	58500	0	6	No	No
33	Female	No	153000	27600	4	No	No
33	Female	Yes	86800	48800	4	No	No
42	Male	Yes	46400	30300	4	No	No
28	Female	No	36900	57700	6	Yes	No
27	Female	Yes	46900	29200	3	No	No
35	Male	No	57400	16600	2	Yes	No
31	Female	No	91200	16800	5	No	No
32	Female	Yes	62100	21400	8	Yes	No
34	Male	Yes	38800	12500	7	No	No
24	Female	Yes	90200	49300	13	Yes	No
30	Male	Yes	47100	9100	5	No	No
28	Male	Yes	159200	19200	8	No	No
32	Female	Yes	52700	15900	5	Yes	No
34	Male	No	73400	40200	13	Yes	No
31	Male	No	58900	55800	5	Yes	No
33	Male	Yes	81100	27200	3	Yes	No
31	Female	Yes	68400	20100	4	Yes	No
29	Male	Yes	55700	17300	3	No	No
25	Male	No	45400	42100	7	Yes	No
29	Male	No	59600	39500	5	No	No
25	Female	Yes	47700	21400	2	No	No
30	Female	Yes	57200	10200	11	No	No
28	Female	Yes	47300	18300	11	Yes	No
32	Female	Yes	58300	20600	4	No	No
34	Female	Yes	47800	63400	17	No	No
33	Female	No	61600	38200	5	Yes	No
24	Male	Yes	64000	50400	7	No	No
30	Female	Yes	87400	9500	5	No	No
25	Male	Yes	56200	27900	6	No	No
26	Male	No	100600	18100	4	No	No
31	Male	No	51100	39500	5	No	No
29	Male	No	90100	23400	5	No	No
31	Male	Yes	50800	34100	6	No	No
36	Male	No	62500	17500	6	No	No
34	Female	No	37400	12600	7	Yes	No
24	Male	No	102700	29200	3	No	No
28	Male	No	68400	42600	4	Yes	No
34	Female	No	68800	18100	4	Yes	No
31	Male	No	108000	11200	7	No	No
31	Male	No	200500	30500	9	Yes	No
30	Male	No	123000	39300	9	No	No
38	Female	Yes	64300	23100	7	No	No
29	Male	No	72600	38400	2	No	No
21	Male	No	81500	35300	6	Yes	No
32	Female	Yes	57000	15800	3	No	No
27	Male	No	101500	24300	6	Yes	No
29	Male	No	67600	24700	2	Yes	No
32	Male	No	70200	30800	7	No	No
32	Male	No	64800	17400	3	Yes	No
29	Female	No	70800	9100	2	No	No
35	Male	Yes	50300	23300	2	Yes	No
36	Male	Yes	30300	15000	2	Yes	No
32	Male	Yes	61700	0	14	No	No
25	Female	No	103500	31300	7	Yes	No
29	Male	No	33400	34500	8	Yes	No
22	Male	No	51700	26300	7	Yes	No
28	Male	Yes	76400	21900	7	No	No
29	Female	Yes	47400	27100	7	Yes	No
29	Male	Yes	118800	59300	11	No	No
29	Female	Yes	61300	34500	9	No	No
32	Female	No	97900	63200	8	Yes	No
30	Male	Yes	67400	7000	3	No	No
29	Female	No	82000	18100	7	No	No
30	Female	No	60700	15500	5	No	No
38	Male	Yes	98800	11800	4	Yes	No
32	Female	No	61800	27700	3	Yes	No
27	Male	Yes	49600	14600	6	No	No
29	Male	Yes	54700	17500	3	No	No
28	Female	No	153300	37900	7	Yes	No
33	Male	Yes	94400	13800	9	Yes	No
32	Male	Yes	39500	22100	9	Yes	No
35	Female	Yes	72400	24200	6	Yes	No
27	Male	Yes	93200	19500	6	Yes	No
29	Male	No	161400	23300	4	Yes	No
30	Male	No	56100	29000	5	No	No
34	Female	Yes	95000	53200	5	No	No
24	Male	Yes	94100	15300	6	No	No
30	Female	Yes	24300	25800	8	Yes	No
28	Male	No	49400	34200	4	No	No
23	Female	No	41200	25000	7	No	No
26	Female	No	81800	24500	7	Yes	No
30	Male	No	62400	25500	6	No	No
26	Male	Yes	117800	19400	14	No	No
24	Female	Yes	100100	30600	11	No	No
33	Female	Yes	94100	21100	9	No	No
30	Female	Yes	59300	83300	13	No	No
25	Female	Yes	89500	50700	5	Yes	No
24	Male	Yes	88900	29600	2	No	No
35	Male	No	53200	29700	6	Yes	No
34	Female	No	58600	12100	6	Yes	No
36	Male	No	54200	25000	2	No	No
29	Male	No	38500	37200	5	No	No
27	Female	Yes	69800	16600	1	No	No
30	Male	No	66200	58000	2	No	No
25	Male	No	78900	23400	4	Yes	No
32	Male	No	87200	21500	3	Yes	No
29	Male	No	79300	33800	15	Yes	No
27	Male	No	51800	18400	7	No	No
27	Male	No	70900	13100	11	Yes	No
33	Male	No	110900	18100	18	No	No
29	Male	Yes	109400	34300	2	Yes	No
30	Male	No	43800	23500	8	Yes	No
32	Male	Yes	49700	19200	6	Yes	No
23	Female	Yes	149300	16900	4	Yes	No
26	Male	No	68900	22100	5	No	No
34	Female	No	50100	27000	3	Yes	No
35	Male	Yes	32400	65200	2	Yes	No
31	Female	Yes	82700	11200	5	Yes	No
29	Female	Yes	104300	24800	12	No	No
25	Male	No	49600	46500	9	Yes	No
34	Male	No	36500	20000	7	Yes	No
38	Female	Yes	65500	16200	1	No	No
34	Male	Yes	110800	27200	9	No	No
32	Female	No	38100	11100	3	No	No
33	Female	Yes	70700	18500	2	Yes	No
27	Male	Yes	39800	21300	1	No	Yes
30	Male	Yes	60600	19400	3	No	Yes
32	Female	Yes	48200	17000	5	Yes	No
33	Male	Yes	108700	28700	4	No	No
26	Female	Yes	71300	20700	4	Yes	No
29	Male	Yes	110800	17100	4	No	Yes
36	Male	Yes	120300	21000	5	No	Yes
38	Male	Yes	130000	21900	6	Yes	Yes
31	Female	Yes	60300	61200	7	Yes	Yes
31	Female	No	70300	10200	8	No	No
31	Male	No	100700	23600	5	Yes	No
30	Male	Yes	72300	23900	4	No	No
30	Male	No	45800	28100	5	No	Yes
24	Male	Yes	51600	23600	6	No	No
34	Male	No	48200	70800	10	No	Yes
39	Male	Yes	87900	25100	14	No	No
27	Male	No	89600	22300	7	No	No
31	Female	Yes	56100	36200	6	Yes	Yes
32	Male	Yes	93600	20600	12	Yes	Yes
37	Male	Yes	100300	38300	4	Yes	No
29	Male	No	96000	13800	5	No	No
31	Male	No	105500	47000	10	Yes	Yes
27	Male	No	76400	30300	4	No	No
31	Female	Yes	77100	37100	6	Yes	Yes
32	Female	Yes	62300	64100	4	Yes	Yes
30	Male	No	52700	19300	6	Yes	No
26	Female	No	59000	27400	4	Yes	Yes
32	Female	No	42200	23900	2	Yes	Yes
32	Female	No	83500	27400	7	No	Yes
26	Female	Yes	28200	14400	3	Yes	Yes
24	Male	No	103500	36000	4	Yes	Yes
25	Female	No	35100	30300	6	Yes	No
28	Female	Yes	36800	30500	11	Yes	Yes

You are given data regarding subscribers to a magazine about real estate. The data gathered by taking a random sample of subscribers and then sending out questionnaires. The data includes the following variables: Age of the subscriber Gender of the subscriber (m/f) Household had children (yes/no) Household income Total financial investments (non-real-estate) Number of financial transactions made last year (including stocks, bonds and mutual funds but not real estate) Will they buy real estate within the next year? (yes/no) Will they buy an electric car in the next two years? (yes/no)

Write a report that describes a typical customer that subscribes to this magazine. The report should include at a minimum the following: (Data can be found in the file Real estate magazinePreview the document)

95% confidence interval of total financial investments (non real-estate)

95% confidence interval of proportion of customers who will buy an electric car within the next two years

95% confidence interval of household income

95% confidence interval of proportion of customers who are going to buy real estate within the next year

Answer 1

*****

95% confidence interval of total financial investments (non real-estate)

Solution:

Confidence interval = Xbar ± t*S/sqrt(n)

From given data, we have

Sample mean = Xbar = 28538.29268

Sample standard deviation = S = 15810.83074

Sample size = n = 410

Confidence level = 95%

Degrees of freedom = n – 1 = 409

Critical t value = 1.9658

(by using t-table)

Confidence interval = 28538.29268 ± 1.9658*15810.83074/sqrt(410)

Lower limit = 28538.29268 - 1.9658*15810.83074/sqrt(410)

Lower limit = 28538.29268 - 1534.9629 = 27003.33

Upper limit = 28538.29268 + 1.9658*15810.83074/sqrt(410)

Upper limit = 28538.29268 + 1534.9629

Confidence interval = (27003.33, 30073.26)

We are 95% confident that the average financial investment in non real estate will lies between $27, 003 and $30,073 approximately.

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95% confidence interval of proportion of customers who will buy an electric car within the next two years

Confidence interval = P ± Z*sqrt(P*(1 – P)/n)

From given data, we have

X = 128, n = 410, so P = X/n = 128/410 = 0.312195122

Confidence level = 95%

Critical Z value = 1.96

Confidence interval = 0.31219512 ± 1.96*sqrt(0.312195122*(1 - 0.312195122)/410)

Confidence interval = 0.31219512 ± 0.0449

Lower limit = 0.31219512 - 0.0449 = 0.2673

Upper limit = 0.31219512 + 0.0449 = 0.3570

We are 95% confident that the population proportion of the customers who will buy an electric car will lies between 26.73% and 35.70%.

*****

95% confidence interval of household income

Confidence interval = Xbar ± t*S/sqrt(n)

From given data, we have

Sample mean = Xbar = 74459.5122

Sample standard deviation = S = 34818.21067

Sample size = n = 410

Confidence level = 95%

Degrees of freedom = n – 1 = 409

Critical t value = 1.9658

(by using t-table)

Confidence interval = 74459.5122 ± 1.9658*34818.21067/sqrt(410)

Confidence interval = 74459.5122 ± 3380.2565

Lower limit = 74459.5122 - 3380.2565 = 71079.26

Upper limit = 74459.5122 + 3380.2565 = 77839.77

We are 95% confident that the average household income will be lies between $71079.26 and $77839.77.

*****

95% confidence interval of proportion of customers who are going to buy real estate within the next year

Confidence interval = P ± Z*sqrt(P*(1 – P)/n)

From given data, we have

X = 181, n = 410, so P = X/n =181/410 = 0.441463415

Confidence level = 95%

Critical Z value = 1.96

Confidence interval = 0.441463415 ± 1.96*sqrt(0.441463415*(1 - 0.441463415)/410)

Confidence interval = 0.441463415 ± 0.0481

Lower limit = 0.441463415 - 0.0481 = 0.3934

Upper limit = 0.441463415 + 0.0481 = 0.4895

We are 95% confident that the proportion of customers who are going to buy real estate is lies between two proportion value 0.3934 and 0.4895.