Homework SourseCaculate the standard deviation for the 9 values Enter your
Caculate the standard deviation for the 9 values. Enter your result with only one sig fig, and remeber to use a zero before the decimal point for values less than 1.
37.120
37.666
37.302
37.394
37.361
37.191
37.775
37.606
37.498
336.913/9 = 37.43478 and this the part where i get lost. is the answer 0.655 ?
Using the Average and standard deviations calculated for the basket masses, give the lower and upper mass limits where we can expect to measure 68% or additional basket masses.
68% lower limit
68% upper limit
Again using the average and standard deviations caculated for the basket masses, give the lower and upper mass limits where we can expect to measure 99.7% of additional basket masses
99.7% lower limit
99.7% upper limit
Solution
Getting the mean, X,
X = Sum(x) / n
Sum(x) = 336.913
As n = 9
Thus,
X = 37.43477778
Setting up tables,
x x - X (x - X)^2
37.12 -0.314777778 0.099085049
37.666 0.231222222 0.053463716
37.302 -0.132777778 0.017629938
37.394 -0.040777778 0.001662827
37.361 -0.073777778 0.00544316
37.191 -0.243777778 0.059427605
37.775 0.340222222 0.11575116
37.606 0.171222222 0.029317049
37.498 0.063222222 0.003997049
Thus, Sum(x - X)^2 = 0.385777556
Thus, as
s^2 = Sum(x - X)^2 / (n - 1)
As n = 9
s^2 = 0.048222194
Thus,
s = 0.219595525 = 0.2 [ANSWER, STANDARD DEVIATION]
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Thus, by empirical rule, 68% lie within one standard deviation, that is,
68% lower limit = X - s = 37.43 - 0.22 = 37.21 [ANSWER]
68% upper limit = X + s = 37.43 + 0.22 = 37.65 [ANSWER]
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Thus, by empirical rule, 99.7% lie within three standard deviations, that is,
99.7% lower limit = X - 3s = 37.43 - 3*0.22 = 36.77 [ANSWER]
99.7% upper limit = X + 3s = 37.43 + 3*0.22 = 38.09 [ANSWER]
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