Question

1. In excel, list the values of your bill for the last 12 months on one column.
2. Find the sample mean and sample standard deviation of your data.
3. Pick three bills from the last 12 months and change the values into z-scores. What does the z-score tell you about that particular month?

Analysis

1. Between what two values would be considered a normal bill? Remember, being within 2 Standard Deviations is considered normal.
2. Are any of your bills in the last 12 months unusual? Very unusual?
3. Are there times when you would accept an "unusual" bill? Explain.

BILL VALUES:

January           $61.34

February         $48.72

March              $58.63

April                $64.24

May                 $59.75

June                 $96.77

July                  $160.64

August             $167.68

September      $195.39

October           $203.13

November       $130.27

December       $68.76

3 bills to change the value into z-score are:

April, July, October

Answer 1

X	Mean, x̅	x-x̅	(x-x̅)²
61.34	109.61	-48.27	2329.9929
48.72	109.61	-60.89	3707.5921
58.63	109.61	-50.98	2598.9604
64.24	109.61	-45.37	2058.4369
59.75	109.61	-49.86	2486.0196
96.77	109.61	-12.84	164.8656
160.64	109.61	51.03	2604.0609
167.68	109.61	58.07	3372.1249
195.39	109.61	85.78	7358.2084
203.13	109.61	93.52	8745.9904
130.27	109.61	20.66	426.8356
68.76	109.61	-40.85	1668.7225

∑x = 1315.32

n = 12

∑(x-x̅)² = 37521.81

Mean, x̅ = Ʃx/n = 1315.32/12 = 109.61

Standard deviation, s = √(Ʃ(x-x̅)²/(n-1)) = √(37521.8102/(12-1)) = 58.4044

For April :

z = (64.24-109.61)/58.4044 = -0.78

z score tells us that this value is 0.77 below the mean.

For July:

z = (160.64-109.61)/58.4044 = 0.87

z score tells us that this value is 0.87 above the mean.

For October:

z = (203.13-109.61)/58.4044 = 1.60

z score tells us that this value is 1.6 above the mean.

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Values that are considered normal =

X1 = 109.61 - 2*58.40 = -7.19 ( as this value is below zero and bill cant be negative so we will assume it 0)

X2 = 109.61 + 2*58.40 = 226.41

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No, None of your bills in the last 12 months is unusual.