Question

To see if a spinner that is divided into 100 equal sections labeled 1 to 100 is fair, a researcher spins the spinner 1000 times and records the result. Let X represent the outcome. The table below shows the probability distribution of the data. Find the mean and the standard deviation of the probability distribution using Excel.

• Round the mean and standard deviation to two decimal places.
  
  "x"   P(x)
  1   0.011
  2   0.011
  3   0.011
  4   0.01
  5   0.008
  6   0.011
  7   0.011
  8   0.01
  9   0.01
  10   0.011
  11   0.011
  12   0.01
  13   0.008
  14   0.01
  15   0.008
  16   0.012
  17   0.006
  18   0.011
  19   0.012
  20   0.009
  21   0.011
  22   0.012
  23   0.01
  24   0.011
  25   0.011
  26   0.01
  27   0.01
  28   0.01
  29   0.012
  30   0.009
  31   0.011
  32   0.011
  33   0.008
  34   0.009
  35   0.009
  36   0.009
  37   0.01
  38   0.008
  39   0.009
  40   0.01
  41   0.012
  42   0.01
  43   0.009
  44   0.009
  45   0.01
  46   0.011
  47   0.01
  48   0.011
  49   0.011
  50   0.011
  51   0.011
  52   0.01
  53   0.007
  54   0.011
  55   0.009
  56   0.01
  57   0.007
  58   0.011
  59   0.011
  60   0.012
  61   0.008
  62   0.011
  63   0.009
  64   0.01
  65   0.01
  66   0.011
  67   0.009
  68   0.01
  69   0.01
  70   0.009
  71   0.01
  72   0.01
  73   0.011
  74   0.008
  75   0.009
  76   0.009
  77   0.011
  78   0.011
  79   0.011
  80   0.009
  81   0.01
  82   0.008
  83   0.009
  84   0.011
  85   0.012
  86   0.01
  87   0.009
  88   0.011
  89   0.01
  90   0.01
  91   0.009
  92   0.011
  93   0.011
  94   0.011
  95   0.008
  96   0.01
  97   0.01
  98   0.01
  99   0.011
  100   0.009

Answer 1

MEAN= E(X)= X*P(x)= 50.277

MEAN=50.28

VARIANCE= E(X^2)- {E(X)}^2

= 3368.351-(50.28)^2

= 3368.351-2528.078

=840.27

S.D= SQRT(840.27)= 28.99