Mathematics: Advanced Statistics

A random sample of 225 students in the biotechnology program at Humber College was selected from the past 5 years and the number of absences from each one was recorded. The results were x = 11.6 and s = 4.1 absences. Estimate the mean number of absences over the past 5 years with 90% confidence.

 

The confidence interval for the average number of observations lies between 2.4 observations and 6.4 observations. Mean = 5.1 + 2.6 + 3.4 + 6.3 + 2.8 + 4.5 + 5.9 + 1.7 + 3.7 + 8.0/10 Mean = 4.4 SD = SQR(5.1 – 4.4)^2 + (2.6 – 4.4)^2 + (3.4 – 4.4)^2 + (6.3 – 4.4)^2 + (2.8 – 4.4)^2 + (4.5 – 4.4)^2 + (5.9 – 4.4)^2 + (1.7 – 4.4)^2 + (3.7 – 4.4)^2 + (8.0 – 4.4)^2/10 SD = 1.94 1 – 0.99 = 0.01 0.01/2 = 0.005 10 – 1 = 9 4.4 + 3.250(1.94/SQR10) = 6.4 obsevations 4.4 – 3.250(1.94/SQR10) = 2.4 observations

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6. Cost-Benefit Analysis – conduct a cost-benefit analysis using the payback method and the net present value method for a project that will require $10,000 in capital outlay, $30,000 in equipment, and $10,000 in training during the first year. Each subsequent year will incur additional labor cost of $5,000 per year, reduce material costs by $15,000, and increase revenue by $20,000 per year. Assume NPV is discounted by 5%. Please include your formula for the payback method and an image of the excel table you create for the net present value method.

7. A ferris wheel has a diameter of 10 m and takes 24 sec to make one revolution. The lowest point on the wheel is 1 m above the ground. (8 marks)

a. Sketch a graph to show how a rider’s height above the ground varies with time as the ferris wheel makes a rotation. Assume the person starts the ride at the lowest point on the wheel.

b. Write a trigonometric equation that describes the graph. (steps are required)

c. Check the accuracy of your equation by using t = 12 sec. Explain why this provides a check of the accuracy of the equation. What are two more values that would provide a good check?

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