2990 people signed up for Ironman Wisconsin in 2015. Of the 2990, 2338 actually
ID: 3376843 • Letter: 2
Question
2990 people signed up for Ironman Wisconsin in 2015. Of the 2990, 2338 actually finished. Data on the finishers is listed below: Finished under _____ hours: Frequency 9 1 9.5 3 10 22 10.5 50 11 101 11.5 117 12 204 12.5 202 13 272 13.5 211 14 199 14.5 205 15 211 15.5 146 16 157 16.5 130 17 107 a. Find the average finish time. b. Find the standard deviation of this distribution. 2990 people signed up for Ironman Wisconsin in 2015. Of the 2990, 2338 actually finished. Data on the finishers is listed below: Finished under _____ hours: Frequency 9 1 9.5 3 10 22 10.5 50 11 101 11.5 117 12 204 12.5 202 13 272 13.5 211 14 199 14.5 205 15 211 15.5 146 16 157 16.5 130 17 107 a. Find the average finish time. b. Find the standard deviation of this distribution. 2990 people signed up for Ironman Wisconsin in 2015. Of the 2990, 2338 actually finished. Data on the finishers is listed below: Finished under _____ hours: Frequency 9 1 9.5 3 10 22 10.5 50 11 101 11.5 117 12 204 12.5 202 13 272 13.5 211 14 199 14.5 205 15 211 15.5 146 16 157 16.5 130 17 107 a. Find the average finish time. b. Find the standard deviation of this distribution.Explanation / Answer
A)
Getting the mean, X,
X = Sum(x) / n
Sum(x) = 2559
As n = 34
Thus,
X = 75.26470588 [ANSWER, AVERAGE FINISH TIME]
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B)
Setting up tables,
x x - X (x - X)^2
9 -66.26470588 4391.011246
1 -74.26470588 5515.24654
9.5 -65.76470588 4324.99654
3 -72.26470588 5222.187716
10 -65.26470588 4259.481834
22 -53.26470588 2837.128893
10.5 -64.76470588 4194.467128
50 -25.26470588 638.3053633
11 -64.26470588 4129.952422
101 25.73529412 662.3053633
11.5 -63.76470588 4065.937716
117 41.73529412 1741.834775
12 -63.26470588 4002.42301
204 128.7352941 16572.77595
12.5 -62.76470588 3939.408304
202 126.7352941 16061.83478
13 -62.26470588 3876.893599
272 196.7352941 38704.77595
13.5 -61.76470588 3814.878893
211 135.7352941 18424.07007
14 -61.26470588 3753.364187
199 123.7352941 15310.42301
14.5 -60.76470588 3692.349481
205 129.7352941 16831.24654
15 -60.26470588 3631.834775
211 135.7352941 18424.07007
15.5 -59.76470588 3571.820069
146 70.73529412 5003.481834
16 -59.26470588 3512.305363
157 81.73529412 6680.658304
16.5 -58.76470588 3453.290657
130 54.73529412 2995.952422
17 -58.26470588 3394.775952
107 31.73529412 1007.128893
Thus, Sum(x - X)^2 = 238642.6176
Thus, as
s^2 = Sum(x - X)^2 / (n - 1)
As n = 34
s^2 = 7231.594474
Thus,
s = 85.03878218 [ANSWER, STANDARD DEVIATION]
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