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Because of the immediate suspension of classes nationwide due to the COVID-19 pandemic, many
schools opted to give the final examination online. The scores on a certain exam are normally
distributed with a mean of 75 and a standard deviation of 10. Find the probability of the score.
a. Less than 54
b. At least 50
c. The average age of the ABS CBN employees is known to be 32 years and the standard
deviation is 5 years. Find the probability that a random sample of 36 employees will have an average
age of less than 30 years.
What is the Fourier cosine series for f(x) = 2-π, in the interval 0 ≤ x < 2π?
In a study of inter spousal aggression and its possible effect on child behavior, the Behavior Problem Checklist (BPC) scores were recorded for 47 children and whose parents were classified as aggressive. The sample mean and standard deviation were 7.92 and 3.45, respectively. For a sample of 38 children whose parents were classified as non-aggressive, the mean and standard deviation of the BPC scores were 5.80 and 2.87, respectively. Do these observations substantiate the conjecture that the children of aggressive families have lower mean BPC than those of non- aggressive families? Use a significance level of 0.05.
12. If the total cost operations (Y) is related to sale (X) , by the equation Y = 0.6x+10,000 find
(a) Fixed cost
(b) Total cost on sales of birr 50,000
(c) The breakeven point
(d) Net profit before taxes on sales of birr 60, 000.
11. A manufacturer has a fixed cost of birr 120,000and a variable cost of birr 20 per unit made and sold. Selling
price is birr 50 per unit.
(a) Write revenue, cost and profit equations using C for cost, Q for number of units and P for profit.
(b) Find the breakeven quantity
(c) Find the breakeven Birr volume of sales (revenue)
(d) Compute profit if 10,000 units are made and sold, 100 units are made and sold.
(e) Construct the breakeven chart. Label the cost, revenue and the fixed Cost line and the breakeven point.
9. ABC merchandising firm plans to work on a margin of 46% of retails and it incurs other variable cost of birr
0.16per birr of sales. A fixed cost equals to birr 25,000.
(a) Find the equation relating total cost to sales?
(b) Find the breakeven point?
(c) What would be net profit before taxes if sales are birr 1000,000?
(d) If the firm wants to make profit before taxes of birr20, 000, what should be the revenue level?
8. A small home business set up with an investment of $ 10,000 for equipment. The business manufactures a
product at a cost of br. 0.64 per unit. If the product sales for Br. 1.20 per unit how many units must be sold
before the business breaks even?
7. In its first year, “Abol Buna Co” had the following experience Sales = 25,000 units
Selling price = br.100 TVC = br.1, 500,000 TFC = br.350, 000. Required:
(a) Develop Revenue, cost & profit functions for the co. in terms of quantity.
(b) Find the Breakeven point in terms of quantity
(c) Convert the cost equation in terms of quantity in to a cost equation in terms of revenue
(d) Find the Breakeven revenue
(e) If profit had been br. 500,000 what would have been the sales volume (revenue) &
the quantity of sales
(f) What would have been the profit if sales are br. 2,000,000?
6. XYZ company’s cost function for the next four months is C = 500,000+5Q
(a) Find the BE dollar volume of sales if the selling price is br. 6 / unit
(b) What would be the company’s cost if it decides to shut down operations for the next four months
(c) If, because of strike, the most the company can produce is br. 100,000 units, should it
shutdown? Why or why not?
5. A contractor purchases a piece of equipment for birr 30,000. The equipment requires an average expenditure
of birr 6 per hour for fuel and maintenance and the operator is paid birr 10 per hour. The customers are
charged birr 20 per hour for the use of the equipment. Required:
(a) Write the total cost, total revenue and total profit functions in terms of the number of
hours the machine is used.
(b) Find the number of hours the equipment must be operated for the contractor to breakeven.
(c) What will be the profit (loss) level if the machine is operated for 8,000hours?
#332078 on Oct 2022