1. Weekly overtime hours by 15 randomly selected custodial staff at State College for the last week of August was: 0 15 20 21 23 25 28 30 36 37 37 40 45 50 73 Find: a) The average overtime hours worked for a custodial person. (3 marks) b) The median of the overtime hours worked. (3 marks) The standard deviation of the overtime hours worked. (4 marks) Based on the results of a and b comment on which measurement you feel would be most useful for measuring central tendency for the custodial staff at State College. (3 marks) 2. The following information is available on the amount of time (in minutes) 100 customers were put on hold before their calls to a company's Customer Service 800-number were answered: Note: this is grouped (histogram) data. Class # Class (minutes) # of Customers 0 and under 2 52 2 and under 4 20 4 and under 6 15 6 and under 8 9 8 and under 10 4 Total 100 a) What is the approximate average amount of time customers were put on hold? (2 marks) b) What is the approximate standard deviation of the time customers were put on hold? (2 marks) c) What percentage of customers were put on hold for greater than 8 minutes? (2 marks)d) What percentage of customers were put on hold for 6 minutes or less? (1 marks) 3. The following table presents monthly seasonal indexes for the cost of abushel of grapefruits in a certain county in Florida. m a) Interpret the seasonal index for September. (1 marks) h) From the original historical data (1999 - 2003) a trend line of TRt = $5.50 + $0.23t, where t = l to 60, was calculated. Assuming a multiplicative seasonal model forecast the cost of a bushel of g-rapefruits for each of the first six months of 2004. (6 marks) 4. The Cost of delivery for a local courier for each parcel is $0.96 and the courier has monthly xed costs they must absorb which are $3,600. If they can charge $4.80 per parcel then determine the following: a) What are the courier's linear cost, revenue and prot equations? (6 marks) 13) How many parcels must be delivered in order for the rm to breakeven? (2 marks) 5. A company sells its products in a market where the market price, p, is linked to the quantity sold, q, by the linear equation p = 120 2g. a) Calculate the market price if the company sells 50 units. What is the revenue equation and the revenue if company sells 50 units? (3 marks) The company incurs fixed costs of $400 and an additional cost of $12 for each unit produced. b) What is the cost equation? How much will it cost to produce 50 units? (3 marks) c) What is the prot equation? What prot will the company make from producing and selling 50 units? (3 marks) d) Calculate the number of units that will maximize the prot. What is the corresponding market price that will maximize prot? What is the maximum prot? (4 marks) 6. Jane's monthly income from her part-time job was $1200 in 2013 and $2236 in 2013. Given that the CPI for 2013 was 100.0 and 111.5 for 2018, a) Determine the purchasing power of the dollar for 2018 (2 marks) b) Determine Jane's real income for 2018 (2 marks) c) Comment on Jane's purchasing power in 2018 relative to 2013 (2 marks) 7. Property taxes for an Ontario resident over the years are listed. Year (x): 2007 2003 2009 2010 2011 2012 Taxes(y): $2,900 $3,000 $3,150 $3,300 $3,400 $3,600 a) Drawr'sketch a scatter diagram. (3 marks) b) Calculate the least squares equation (simple linear regression). Let 200':Ir = 1, 2008 =2 etc. (4 marks) c) Predict the property tax for the year 2020. (2 marks) 8. A Company produces two types of widgets, manual and electric. Each requires in its manufacture the use of three machines, A, B and C. Each manual widget requires the use of machine A for 2 hours, machine B for 1 hour and machine C for 1 hour. An electric widget requires 1 hour on A, 2 hours on B, and 1 hour on C. Furthermore, suppose the maximum number of hours available per month for the use of the machines A, B and C are 180, 160, and 100 respectively. The prot on a manual widget is $4 and on an electric widget it is $6. a) Determine the maximum prot equation. (2 marks) b) Set up the system of inequalities. (4 marks) c) Graphfsketch and identify the feasible region. (3 marks) d) Identify (showing calculations for each) all applicable corner points. If the company can sell all the widgets they can produce, how many of each type should it make in order to maximize profit? (6 marks)