Part 1:
- My name is ASTBURY. The first three letters of my last name are AST. Each of these letters has its place value in the alphabet. A is 1, S is 19, and T is 20. By adding the three values together we get:
1 + 19 + 20 = 40
Therefore the sum is forty
- My yearly income for Week Four Discussion 1is:
40 × $1,500 = $60,000
Therefore my yearly income is sixty thousand dollars.
- By using the following monthly expenses: Car payment = $283.15, Car insurance = $72, Utilities (includes water and power) = $242.77, Internet = $32, and Cell Phone = $79.95, I can calculate the total monthly expenses as shown below:
$283.15 + $72 + $242.77 + $32 + $79.95 = $709.87
Therefore monthly expenses amount to seven hundred and nine, point eight seven dollars.
- The yearly educational bill amounts to $7980. Monthly educational bill amounts to $7980 ÷ 12 = $665 (Six hundred and sixty-five dollars)
- My monthly income amounts to:
$60,000 ÷ 12 = $5,000
Therefore the monthly income is five thousand dollars.
- What percent of your monthly income is the car payment? This is expressed as:
Therefore the percentage of my monthly income as the car payment is five point six six three percent.
- Income available to spend for food, clothing, and rent or mortgage amounts to:
Monthly income – Monthly expenses = $5,000 – ($709.87 + $665)
= $5,000 - $1,374.87
= $3,625.13
This amount in words is, three thousand, six hundred and twenty-five point one three. This can be expressed in percentage as follows:
Experts have suggested that an individual can afford to pay 28% of his or her gross monthly income for a home mortgage. Therefore 28% of my monthly income is calculated as:
0.28 × $5,000 = $1,400 (One thousand, four hundred dollars)
Thus I can afford a monthly mortgage payment of $1,400.
So that to know what I can afford to borrow, we look up the number corresponding to 7% and 25 years in Table 9-1. An equation set up and the value for y is calculated.
7.70y = $1,400
y = $1,400 ÷ 7.70
y = $181.82
The value of y is multiplied by 1000 because the payments in Table 9-1 are per $1,000.00 of the mortgage.
$181.82 × 1,000 = $181,820 (One hundred and eighty-one thousand, eight hundred and twenty)
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Thus, I can afford a mortgage of $181,820.
- Assume you can afford a down payment equal to 25% of your yearly income. What is the total purchase price can you afford for a home? Would this amount allow you to purchase a home in the area where you live?
Down payment is calculated as:
The total purchase price I can afford for a home is,
$181,820 + $15,000 = $196,820 (One hundred and ninety-six thousand, eight hundred and twenty dollars)
This amount can allow me purchase a home within the area where I live.
Part 2
- Differences between classical and empirical probability.
- According to Spiegel & Schiller (2008), in classical probability, the total number of ways an event can be observed is divided by the total number of events which can occur whereas in empirical probability the total number of times an event is observed, is divided by the total number of trials carried on.
- According to Spiegel & Schiller (2008), empirical probability is the kind of probability that is derived from real experience while a theoretical probability is the kind of probability derived from mere thinking.
- Experiment of tossing coins
- 18 coins are tossed ten times
TRIALS | 1^{ST} | 2^{ND} | 3^{RD} | 4^{TH} | 5^{TH} | 6^{TH} | 7^{TH} | 8^{TH} | 9^{TH} | 10^{TH} | |
OUTCOMES |
H | 10 | 9 | 10 | 11 | 7 | 11 | 10 | 8 | 11 | 9 |
T | 8 | 9 | 8 | 7 | 11 | 7 | 8 | 10 | 7 | 9 |
KEY:
H-Head
T-Tail
- Total number of possibilities is expressed by 2^{n}^{ }where n is the number of coins
Therefore a total number of possibilities of tossing 18 coins at once are:
2^{18} = 262144
Probability of tossing a head =
Probability of tossing a tail =
- Two of the ten repetitions came out to have exactly the same number of heads and tails, that is, nine heads and nine tails.
- It could not be ½ and ½ because the number of coins exceeded one. The occurrence of a head or a tail when two or more coins are tossed cannot give the probability of ½ but if one coin is tossed then the probability of a head or a tail occurring is ½.
- This experiment is an example of empirical probability.
- The average number of heads from the ten trials can be computed as follows:
Total number of heads for the ten trials is 96
Average number of heads =
=
= 9.6
- Number coins used in the ten trials is equal to 18 x 10 = 180
Average probability =
- Nothing surprising or unexpected happened during the experiment.
- Write the sample space for the outcomes of tossing three coins using H for heads and T for tails.
- HHH, HHT, HTH, HTT, THH, THT, TTH, TTT
- Probability of each of the outcomes is 1/8 = 13%
- This kind of probability is known as theoretical probability.
- We can just draw a probability tree and come up with all these events. Therefore we don’t need to have the coins actually.