Question

Problem 1   

  A survey of 1000 college students shows what they like to do with their time   

  Below is are the results of the survey   

  Activity Percentage   

  Attending College 9%   

  Sleeping 24%   

  Socializing 51%   

  Studying 7%   

  Working 9%   

  Answer the following questions based on the data above   

  a. Construct a bar chart, a pie chart and a Pareto Chart. Place the charts starting in column H   

  b. Which graphical method do you think is best for portraying the data presented above? Why?   

Problem 2   

  The data below is quarterly sales tax revenues submitted to the Texas State government by selected business from the city of Irving, TX.

  Tax Revenues   

$ 10,300.00

$ 11,100.00   

$ 9,600.00

$ 9,000.00

$ 14,500.00

$ 13,000.00

$ 6,700.00

$ 11,000.00

$ 8,400.00

$ 10,300.00

$ 13,000.00   

$ 11,200.00

$ 7,300.00

$ 5,300.00

$ 12,500.00

$ 8,000.00

$ 11,800.00

$ 8,700.00

$ 10,600.00

$ 9,500.00

$ 11,100.00

$ 10,200.00

$ 11,100.00

$ 9,900.00

$ 9,800.00

$ 11,600.00

$ 15,100.00

$ 12,500.00

$ 6,500.00

$ 7,500.00

$ 10,000.00

$ 12,900.00

$ 9,200.00

$ 10,000.00

$ 12,800.00

$ 12,500.00

$ 9,300.00

$ 10,400.00

$ 12,700.00

$ 10,500.00

$ 9,300.00

$ 11,500.00

$ 10,700.00

$ 11,600.00

$ 7,800.00

$ 10,500.00

$ 7,600.00

$ 10,100.00

$ 8,900.00

$ 8,600.00

a. Compute mean, mode, median and standard deviation for the population data given Place the answers clearly below labeling each statistic

b. What percentage of the businesses have their taxes within plus or minus 1, 2 or 3 standard deviations Does this follow our normally accepted distributions of data? Why or why not? Place your answers below clearly labeling any statistics

  

  

  

Answer 1

1)

a)

b)

bar graph is best for portraying the data presented above as it is to interpret the bar graph

....................

2)

a)

total = 514000

N = 50

mean = $10280

Median = 10300
Mode = 11100
Standard Deviation = 2045.004

b)

x1, x2 = µ +-1σ = 12325, 8234.996

now,

µ =    10280                              
σ =    2045.004                              
we need to calculate probability for ,                                  
P (   12325   < X <   8234.996   )                  
=P( (12325-10280)/2045.004 < (X-µ)/σ < (8234.996-10280)/2045.004 )                                  
                                  
P (    1.000   < Z <    -1.000   )                   
= P ( Z <    -1.000   ) - P ( Z <   1.000   ) =    0.1587   -    0.8413   =    -0.6827

= -68.27% (plus minus 1 std dev)

.........

µ =    10280                              
σ =    2045.004                              
we need to calculate probability for ,                                  
P (   14370.008   < X <   6189.992   )                  
=P( (14370.008-10280)/2045.004 < (X-µ)/σ < (6189.992-10280)/2045.004 )                                  
                                  
P (    2.000   < Z <    -2.000   )                   
= P ( Z <    -2.000   ) - P ( Z <   2.000   ) =    0.0228   -    0.9772   =    -0.9545

-95.45% (plus minus 2 std dev)
..............

µ =    10280                              
σ =    2045.004                              
we need to calculate probability for ,                                  
P (   16415   < X <   4145   )                  
=P( (16415-10280)/2045.004 < (X-µ)/σ < (4145-10280)/2045.004 )                                  
                                  
P (    3.000   < Z <    -3.000   )                   
= P ( Z <    -3.000   ) - P ( Z <   3.000   ) =    0.0013   -    0.9987   =    -0.9973

-99.73% (plus minus 3 std dev)