Determine the probability that the sales will be greater than R50 000 over the 6 month period as a…

Question

Determine the probability that the sales will be greater than R50 000 over the 6 month period as a percentage, rounded off to two decimal places.

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Here are the solutions to your questions:

1.1.1

Identify the sales for each month from the "Income" table.
- January: R58 880
- February: R57 650
- March: R61 340
- April: R50 070
- May: R46 660
- June: R45 390
Compare the sales figures to find the highest value.
The highest sales figure is R61 340, which occurred in March.

The business made more money in March.

1.1.2
Sum the sales from January to June.
$\text{Total Sales} = \text{R}58\,880 + \text{R}57\,650 + \text{R}61\,340 + \text{R}50\,070 + \text{R}46\,660 + \text{R}45\,390$ $\text{Total Sales} = \text{R}329\,990$
Add the Interest from Investments to the Total Sales to find the Total Income (A).
$\text{A} = \text{Total Sales} + \text{Interest from Investments}$ $\text{A} = \text{R}329\,990 + \text{R}87\,430$ $\text{A} = \text{R}417\,420$
The value of A, the total income, is $\boxed{\text{R}417\,420}$ .

1.1.3
Sum all known expenditure items (excluding Salaries B).
$\text{Known Expenditures} = \text{Rent} + \text{Truck Rental} + \text{Insurance} + \text{Fuel} + \text{Consumables}$ $\text{Known Expenditures} = \text{R}30\,000 + \text{R}57\,180 + \text{R}59\,187 + \text{R}18\,200 + \text{R}38\,550$ $\text{Known Expenditures} = \text{R}203\,117$
Subtract the known expenditures from the Total Expenditure to find B (Total Salaries).
$\text{Total Expenditure} = \text{Known Expenditures} + \text{B}$ $\text{R}284\,117 = \text{R}203\,117 + \text{B}$ $\text{B} = \text{R}284\,117 - \text{R}203\,117$ $\text{B} = \text{R}81\,000$
Calculate the salaries per month by dividing B by 6 months.
$\text{Salaries per month} = \frac{\text{B}}{6}$ $\text{Salaries per month} = \frac{\text{R}81\,000}{6}$ $\text{Salaries per month} = \text{R}13\,500$
The value of B is $\boxed{\text{R}81\,000}$ , and the money spent on salaries per month is $\boxed{\text{R}13\,500}$ .

1.1.4
Identify the months where sales were greater than R50 000.
- January: R58 880 (> R50 000)
- February: R57 650 (> R50 000)
- March: R61 340 (> R50 000)
- April: R50 070 (> R50 000)
- May: R46 660 (< R50 000)
- June: R45 390 (< R50 000) There are 4 months with sales greater than R50 000.
Calculate the probability as a fraction.
$\text{Probability} = \frac{\text{Number of months with sales} > \text{R}50\,000}{\text{Total number of months}}$ $\text{Probability} = \frac{4}{6} = \frac{2}{3}$
Convert the probability to a percentage, rounded to two decimal places.
$\text{Percentage} = \frac{2}{3} \times 100\%$ $\text{Percentage} \approx 66.666...\%$ $\text{Percentage} \approx 66.67\%$
The probability that the sales will be greater than R50 000 is $\boxed{66.67\%}$ .

Determine the probability that the sales will be greater than R50 000 over the 6 month period as a percentage, rounded off to two decimal places.

Step-by-step solution

1.1.1

Identify the sales for each month from the "Income" table.

Compare the sales figures to find the highest value.

1.1.2

Sum the sales from January to June.

Add the Interest from Investments to the Total Sales to find the Total Income (A).

1.1.3

Sum all known expenditure items (excluding Salaries B).

Subtract the known expenditures from the Total Expenditure to find B (Total Salaries).

Calculate the salaries per month by dividing B by 6 months.

1.1.4

Identify the months where sales were greater than R50 000.

Calculate the probability as a fraction.

Convert the probability to a percentage, rounded to two decimal places.

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