(3 points) on an exam with a mean of m = 82, you obtain a score of x



1.    (3 points) On an exam with a mean of M = 82, you obtain a score of X =86.

a.    Would you prefer a standard deviation of s = 2 or s = 10? (Hint: Sketch each distribution and find the location of your score.)

b.    If your score were X = 78, would you prefer s = 2 or s = 10? Explain your answer.



2.  (3 points)   A student was asked to compute the mean and standard deviation for the following sample of n = 5 scores: 81, 87, 89, 86, and 87.  To simplify the arithmetic, the student first subtracted 80 points from each score to obtain a new sample consisting of 1, 7, 9, 6, and 7.  The mean and standard deviation for the new sample were then calculated to be M = 6 and x = 3.  What are the values of the mean and standard deviation for the original sample?

3.  (3 points)   

Calculate SS, variance, and standard deviation for the following population of N = 7 scores: 8, 1, 4, 3, 5, 3, 4. (Note: The definitional formula works well with these scores.)



4.  (3 points) For the following population of N = 6 scores: 5, 0, 9, 3, 8, 5


a.    Sketch a histogram showing the population distribution.



a.    Locate the value of the population mean in your sketch, and make an estimate of the standard deviation (as done in Example, 4.2).


b.    Compute SS, variance, and standard deviation for the population.  (How well does your estimate compare with the actual value of σ?)



5.  (3 points) A distribution has a standard deviation of σ = 12.  Find the z-score for each of the following locations in the distribution.

a.    Above the mean by 3 points.   

b.    Above the mean by 12 points.  

c.    Below the mean by 24 points.  

d.    Below the mean by 18 points.   


6.  (5 points) For a population with a mean of µ = 100 and a standard deviation of 12

a.    Find the z-score for each of the following X values.

X = 106    X = 115    X = 130   

X = 91     

X = 88     

X = 64     

b.    Find the score (X value) that corresponds to each of the following z-scores.

z = – 1.00   

z = – 0.50   

z = 2.00      z = 0.75     

z = 1.50     

z = – 1.25   


7.  (3 points) Find the z-score corresponding to a score of X = 60 for each of the following distributions.

a. µ = 50 and σ = 20                 

b. µ = 50 and σ = 10                 

c. µ = 50 and σ = 5                   

d. µ = 50 and σ = 2                    


8.  (1 point) A score that is 6 points below the mean corresponds to a z-score of z = – 0.50.  What is the population standard deviation?



9.  (3 points) For each of the following, identify the exam score that should lead to the better grade.  In each case, explain your answer.

a.    A score of X = 56, on an exam with µ = 50 and σ = 4, or a score of X = 60 on an exam with µ = 50 and σ = 20.


b.    A score of X = 40, on an exam with µ = 45 and σ = 2, or a score of X = 60 on an exam with µ = 70 and σ = 20.


c.    A score of X = 62, on an exam with µ = 50 and σ = 8, or a score of X = 23 on an an exam with µ = 20 and σ = 2.



1.  For the following set of scores, find the value of each expression.  (5 points)



2.  Construct a frequency distribution table for= the following set of scores.  Include columns for proportion and percentage in your table. (5 points)

Scores: 5, 7, 8, 4, 7, 9, 6, 6, 5, 3, 9, 6, 4, 7, 7, 8, 6, 7, 8, 5



3.  The following scores are the ages for a random sample of n = 30 drivers who were issued speeding tickets in New York during 2008.  Determine the best interval width and place the scores in a grouped frequency distribution table.  From looking at your= table, does in appear the tickets are issued equally across age groups? (5= points)

17,  30,  45,  20,  39,  53,28,  19

24,  21,  34,  38,  22,  29, 64

22,  44,  36,  16,  56,  20, 23,  58

32,  25,  28,  22,  51,  26, 43



No the tickets are not distributed equally among all age groups.


4.  Find the mean, median, and mode for the scores in the following frequency distribution table. (5 points)


  X            f*X       cf


10    1      10      15

  9    2      18      14

  8    3      24      12

  7    3      21      9

  6    4      24      6

  5    2      10      2


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