Question 1154331: Susan keeps track of the number of tickets sold for each play presented at The Community Theater. The mean of her data is 117, and the standard deviation is 47. Within how many standard deviations of the mean do all the values fall? Data: 59, 143, 80, 69, 176, 86, 160, 65, 152, 184 *
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
Original set = {59, 143, 80, 69, 176, 86, 160, 65, 152, 184}
Sorted set = {59, 65, 69, 80, 86, 143, 152, 160, 176, 184}
min = 59 and max = 184
mu = mean = 117
sigma = standard deviation = 47
1 standard deviation from the mean
L = lower bound = mu - 1*sigma = 117-1*47 = 70
U = upper bound = mu + 1*sigma = 117+1*47 = 164
Ask yourself: Do all of the data values fall within the interval  (this is in the form  )? The answer is 'no' because 59, 65, 69, 176, and 184 are outside this range.
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2 standard deviations from the mean
L = lower bound = mu - 2*sigma = 117-2*47 = 23
U = upper bound = mu + 2*sigma = 117+2*47 = 211
The interval is now  . Ask a similar question: Do all of the data values fall within the range ? The answer is 'yes'. This is because L = 23 is smaller than the min = 59, while U = 211 is larger than the max = 184.
Final Answer: 2 standard deviations
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