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   89
2.    The 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%?
3.    If you know the standard deviation, how do you find the variance?
4.    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   $235
Find the standard deviation.
5.    A company has 70 employees whose salaries are summarized in the frequency distribution below.
Salary    Number of Employees
5,001–10,000    8
10,001–15,000    12
15,001–20,000    20
20,001–25,000    17
25,001–30,000    13
a.    Find the standard deviation.
b.    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,   10
7.    Create 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,   1
8.    Answer the following questions using the frequency distribution table you created in No. 7.
a.    Which number(s) had the highest frequency?
b.    How many times did a number of 4 or greater get thrown?
c.    How many times was an odd number thrown?
d.    How many times did a number greater than or equal to 2 and less than or equal to 5 get thrown?
9.    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.
a.    Range
b.    Standard deviation
c.    Variance
Lastly, compare the two sets of results.
Company    Wait times in seconds
Big Burger Company    105    67    78    120    175    115    120    59
The Cheesy Burger    133    124    200    79    101    147    118    125
10.    What does it mean if a graph is normally distributed? What percent of values fall within 1, 2, and 3, standard deviations from the mean?