Susan keeps track of the number of tickets sold for each play presented at the community theater. within how many standard deviations of the mean do all the values fall? 135, 71, 69, 80, 158, 152, 161, 96, 122, 118, 87, 85.

1.52  
First, let's calculate the standard deviation. So first, let's calculate the mean:
 M = (135+71+69+80+158+152+161+96+122+118+87+85)/12
 M = 1334/12 = 111.1666667 
 Now the mean of the squares from the mean. So:
 (135-111.1666667)^2 = 23.83333333^2 = 568.0277778
 (71-111.1666667)^2 = -40.16666667^2 = 1613.361111
 (69-111.1666667)^2 = -42.16666667^2 = 1778.027778
 (80-111.1666667)^2 = -31.16666667^2 = 971.3611111
 (158-111.1666667)^2 = 46.83333333^2 = 2193.361111
 (152-111.1666667)^2 = 40.83333333^2 = 1667.361111
 (161-111.1666667)^2 = 49.83333333^2 = 2483.361111
 (96-111.1666667)^2 = -15.16666667^2 = 230.0277778
 (122-111.1666667)^2 = 10.83333333^2 = 117.3611111
 (118-111.1666667)^2 = 6.833333333^2 = 46.69444444
 (87-111.1666667)^2 = -24.16666667^2 = 584.0277778
 (85-111.1666667)^2 = -26.16666667^2 = 684.6944444 
 And their mean:
 (568.0277778+1613.361111+1778.027778+971.3611111+2193.361111+1667
.361111+2483.361111+230.0277778+117.3611111+46.69444444+584.027777
8+684.6944444)/12
 = 12937.66667/12 = 1078.138889 
 And finally, the square root:
 SDEV = sqrt(1078.138889)
 SDEV = 32.83502534 
 So the mean is 111.1666667 and the standard deviation is 32.83502534. 
 Let's determine how far from the mean the lowest and highest values are:
 Low 69 = 69 - 111.1666667 = -42.16666667
 High 161 = 161 - 111.1666667 = 49.83333333 
 The high value is further away from the mean than the low value. The
number of standard deviations from the mean si:
 49.83333333 / 32.83502534 = 1.517688286 
 Rounding to 3 figures gives an answer of 1.52

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