Please provide the solution to all the parts. The table below is taken from the
ID: 3349932 • Letter: P
Question
Please provide the solution to all the parts.
The table below is taken from the Australian Bureau of Statistics website. It provides data on mortgage repayment (monthly) by Australian households living in different dwelling structures in the year 2011.
Dwelling Structure
Total occupied private dwellings
Separate house
Semi-detached, row or terrace house, townhouse
Flat, unit or apartment
Mortgage Repayment (monthly)
Total
2 709 429
2 324 546
190 411
187 375
$0-$299
114 197
99 624
7 352
6 694
$300-$449
64 357
57 107
3 749
3 220
$450-$599
60 317
53 545
3 375
3 112
$600-$799
113 616
101 194
6 224
5 765
$800-$999
146 303
129 290
8 227
8 289
$1,000-$1,399
380 790
331 572
23 386
24 761
$1,400-$1,799
400 688
341 557
27 855
30 434
$1,800-$2,399
548 587
464 033
40 573
42 946
$2,400-$2,999
303 184
256 405
22 677
23 635
$3,000-$3,999
261 122
219 568
21 697
19 333
$4,000 and over
175 821
146 771
16 659
11 781
Mortgage repayment not stated
140 447
123 880
8 637
7 405
a) Find the probability that a randomly selected households live in separate house dwelling? 1 mark
b) In a total occupied private dwellings, what is the probability that a randomly selected households make a monthly mortgage repayment of $800-$999? 1 mark
c) What is the probability that a randomly selected households make a monthly mortgage repayment of $1,800-$2,399 or $2,400-$2,999? 1 mark
d) What is the probability that a randomly selected households make a monthly mortgage repayment of $300-$449 in a flat, unit or apartment dwelling structure?
Dwelling Structure
Total occupied private dwellings
Separate house
Semi-detached, row or terrace house, townhouse
Flat, unit or apartment
Mortgage Repayment (monthly)
Total
2 709 429
2 324 546
190 411
187 375
$0-$299
114 197
99 624
7 352
6 694
$300-$449
64 357
57 107
3 749
3 220
$450-$599
60 317
53 545
3 375
3 112
$600-$799
113 616
101 194
6 224
5 765
$800-$999
146 303
129 290
8 227
8 289
$1,000-$1,399
380 790
331 572
23 386
24 761
$1,400-$1,799
400 688
341 557
27 855
30 434
$1,800-$2,399
548 587
464 033
40 573
42 946
$2,400-$2,999
303 184
256 405
22 677
23 635
$3,000-$3,999
261 122
219 568
21 697
19 333
$4,000 and over
175 821
146 771
16 659
11 781
Mortgage repayment not stated
140 447
123 880
8 637
7 405
Explanation / Answer
a) The probability that randomly selected households to live in separate house dwelling:
The total dwellings= 2709429
The total separate house dwellings= 2324546
The probability= 2324546/ 2709429 = 0.857947
b)The probability that randomly selected households to make a monthly mortgage repayment of $800-$999:
The total dwellings= 2709429
The total monthly mortgage payments of $800-999= 146303
The probability = 146303 / 2709429 =0.053998
c) The probability that randomly selected households to make a monthly mortgage repayment of $1,800-$2,399 or $2,400-$2,999:
The total dwellings= 2709429
The total dwellings of $1800-2399 =548587
The total dwellings of $2400-2999 =303184
The total dwellings of $1800-2399 or $2400-2999= 548587+303184= 851771
The probability= 851771 / 2709429 =0.314373
d)The probability that randomly selected households to make a monthly mortgage repayment of $300-$449 in a flat, unit or apartment dwelling structure:
The total dwellings= 2709429
The total monthly mortgage repayment of $300-449 in a flat, unit or apartment dwelling= 3220
The probability= 3220/ 2709429 = 0.001188
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