Answer:
The mean and standard deviation changed to 23.5 and 14.62 respectively, based on all 12 samples.
Step-by-step explanation:
We are given that the Six samples are collected of the number of scanning errors: 36, 14, 21, 39, 11, and 2 errors, per 1,000 scans each.
Representing the data in tabular form;
X
36 36 - 20.5 = 15.5 240.25
14 14 - 20.5 = -6.5 42.25
21 21 - 20.5 = 0.5 0.25
39 39 - 20.5 = 18.5 342.25
11 11 - 20.5 = -9.5 90.25
2 2 - 20.5 = -18.5 <u> 342.25 </u>
Total <u> 1057.5 </u>
Now, the mean of these value is given by;
Mean, =
=
= = 20.5
Standard deviation formula for discrete distribution is given by;
Standard deviation, =
= = 14.54
Now, the manager has six more samples taken:
33, 45, 34, 17, 1, and 29 errors, per 1,000 scans each
So, the modified table would be;
X
36 36 - 23.5 = 12.5 156.25
14 14 - 23.5 = -9.5 90.25
21 21 - 23.5 = -2.5 6.25
39 39 - 23.5 = 15.5 240.25
11 11 - 23.5 = -12.5 156.25
2 2 - 23.5 = -21.5 462.25
33 33 - 23.5 = 9.5 90.25
45 45 - 23.5 = 21.5 462.25
34 34 - 23.5 = 10.5 110.25
17 17 - 23.5 = -6.5 42.25
1 1 - 23.5 = -22.5 506.25
29 29 - 23.5 = 5.5 <u> 30.25 </u>
Total <u> 2353 </u>
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Now, the mean of these value is given by;
Mean, =
=
= = 23.5
Standard deviation formula for discrete distribution is given by;
Standard deviation, =
= = 14.62