# Homework #2 | Mathematics homework help

IE 151 Homework #2

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Homework #2 | Mathematics homework help
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Continue with Microsoft Excel

You are going to turn in one Excel file with each of the problems on another spreadsheet within the file, unless stated otherwise.

1)      We are looking at the difference in the average rain per month between New Mexico and Arizona.  We think that the amount of rain over the course of a year should be similar to each other, specifically around Las Cruces (for New Mexico) and Tucson (for Arizona).  The data collected (in inches) is as follows:

 Month New Mexico Arizona January 0.51 1.02 February 0.39 0.94 March 0.24 0.87 April 0.28 0.31 May 0.39 0.2 June 0.67 0.28 July 1.54 1.93 August 2.2 2.24 September 1.34 1.22 October 0.94 1.22 November 0.47 0.67 December 0.79 1.02

Data Source: www.usclimatedata.com

Construct a box plot and comment if the amounts of rain are similar to each other for the two areas for a year.

2)      Calculate the following probabilities with the corresponding distribution:

·         Normal Distribution, using a mean of 20 and standard deviation of 10:

o   Find a = 12, not cumulative

o   Find a = 23, cumulative

o

o

·         Poisson Distribution, using a rate equal to 15:

o   Find a = 14, not cumulative

o   Find a = 19, cumulative

o

o

·         Gamma Distribution, using a shape parameter of 5 and scale parameter of 2:

o   Find a = 10, not cumulative

o   Find a = 15, cumulative

o

o

3)      We are conducting an experiment with different levels of factors and how they affect the height that a plant will grow.  Each of the different scenarios are conducted twice, to help ensure more accurate results.  The first factor that was looked at was the amount of yellow light, and had two levels, 50% and 60%.  The second factor that was considered was the amount of red light, and three levels were considered, 10%, 15%, and 20%.  The last factor was the amount of blue light, 5%, 10%, and 15%.  Any remaining light is filtered sun light.  The observations that were witnesses are as follows:

 Yellow Light Red Light Blue Light Observations 50% 10% 5% 12,13 50% 10% 10% 14,15 50% 10% 15% 15,15 50% 15% 5% 12,11 50% 15% 10% 11,13 50% 15% 15% 13,12 50% 20% 5% 15,16 50% 20% 10% 16,15 50% 20% 15% 14,15 60% 10% 5% 10,10 60% 10% 10% 11,12 60% 10% 15% 15,13 60% 15% 5% 13,12 60% 15% 10% 12,10 60% 15% 15% 10,11 60% 20% 5% 14,15 60% 20% 10% 13,15 60% 20% 15% 14,13

Using pivot tables, answer the following questions:

·         What is the overall average of the observations?

·         Regardless of the amount of yellow light, what is the average height if we use 15% red light and 5% blue light?

·         What is the overall maximum value of the data?

·         What is the overall minimum value of the data?

4)      We are working for a company that builds machinery for mining.  There are a certain number of factors that we use in order for use to sell the machinery.  The company has been keeping track of the sales numbers for the past six months, and they would like a number of questions answered.  The sales figures are as follows:

·         August 2014 – \$4,565,853.22

·         September 2014 – \$5,263,558.15

·         October 2014 – \$6,187,998.38

·         November 2014 – \$4,962,347.75

·         December 2014 – \$4,248,654.46

·         January 2015 – \$3,956,874.59

The amount of the money spent on different operations in the company are described as follows:

·         Administrative Expenses are worth 10%

·         Overhead (Rent, Utility Bills, etc.) are worth 15%

·         Marketing gets a budget of 10%

·         Employees earn a commission of 5% of the total sales

·         The profit margin then becomes 60%

There is also an opportunity for our office to earn a bonus from the sales.  However, the amount of the bonus is dependent on the amount of sales.  The amount of bonus is calculated as:

·         If sales are above or equal to \$6,000,000, then a bonus of \$100,000 is given

·         If sales are below \$6,000,000, but above or equal to \$4,500,000, a bonus of \$50,000 is given

·         If sales are below \$4,500,000, then no bonus is given

·         Hint: You are going to need to use two IF functions in one formula

By using a what-if analysis, management wants to know, what do the following values need to change to if we are wanting to make a profit of \$6,500,000? (It’s ok to put your answers on another spreadsheet)

a.       If we are to change the profit margin percentage, what does it need to be?

b.      If we are to change the administrative percentage, what does it need to be?

c.       If we are to change the commission percentage, what does it need to be?