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Math (Prof. Frank ONLY)

This is a 3 part question it is the case, slp & Threaded discusiion all posted below.Frequency Distibutions – CaseProblems need to include all required steps and answer(s) for full credit. All answers need to be reduced to lowest terms where possible.Answer the following problems showing your work and explaining (or analyzing) your results.1.    The math grades on the final exam varied greatly. Using the scores below, how many scores were within one standard deviation of the mean? How many scores were within two standard deviations of the mean?99   34   86   57   73   85    91   93   46    96   88   79    68   85   89The scores for math test #3 were normally distributed. If 15 students had a mean score of 74.8% and a standard deviation of 7.57, how many students scored above an 85%?If you know the standard deviation, how do you find the variance?To get the best deal on a stereo system, Louis called eight appliance stores and asked for the cost of a specific model. The prices he was quoted are listed below:$216   $135   $281   $189   $218   $193   $299   $235Find the standard deviation.A company has 70 employees whose salaries are summarized in the frequency distribution below.SalaryNumber of Employees5,001–10,000810,001–15,0001215,001–20,0002020,001–25,0001725,001–30,00013Find the standard deviation.Find the variance.6.  Calculate the mean and variance of the data. Show and explain your steps. Round to the nearest tenth.14,   16,   7,   9,   11,   13,   8,   10Create a frequency distribution table for the number of times a number was rolled on a die. (It may be helpful to print or write out all of the numbers so none are excluded.)3,   5,   1,   6,   1,   2,   2,   6,   3,   4,   5,   1,   1,   3,   4,   2,   1,   6,   5,   3,   4,   2,   1,   3,   2,   4,   6,   5,   3,   1Answer the following questions using the frequency distribution table you created in No. 7.Which number(s) had the highest frequency?How many times did a number of 4 or greater get thrown?How many times was an odd number thrown?How many times did a number greater than or equal to 2 and less than or equal to 5 get thrown?The wait times (in seconds) for fast food service at two burger companies were recorded for quality assurance. Using the data below, find the following for each sample.RangeStandard deviationVarianceLastly, compare the two sets of results.CompanyWait times in secondsBig Burger Company105677812017511512059The Cheesy Burger13312420079101147118125What does it mean if a graph is normally distributed? What percent of values fall within 1, 2, and 3, standard deviations from the mean?SLPContinuing with the data you collected in the Module 1 SLP, write a paper (1–3 pages) including all of the following content:Include your data from Module 1.Create a frequency distribution table for your data. You can use Excelor Word.Calculate the standard deviation.Calculate the variance.Is this a normal distribution? How do you know?What are the implications?Threaded DiscussonThe number of vacation days taken by employees of a company is normally distributed with a mean of 14 days and a standard deviation of 3 days. For the next employee, what is the probability that the number of days of vacation taken is less than 10 days? More than 21 days? Post your solutions to the problems and respond to the solutions posted by your classmates.

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