Answer to Question #143904 in Statistics and Probability for Vladimyr Lubin

Question #143904
(3.3.8) A data set lists weights​ (lb) of plastic discarded by households. The highest weight is 5.64 ​lb, the mean of all of the weights is x=2.112 ​lb, and the standard deviation of the weights is s=1.111 lb.
a. What is the difference between the weight of 5.64 lb and the mean of the​ weights?
b. How many standard deviations is that​ [the difference found in part​ (a)]?
c. Convert the weight of 5.64 lb to a z score.
d. If we consider weights that convert to z scores between -2 and 2 to be neither significantly low nor significantly​ high, is the weight of 5.64 lb​ significant?
1
Expert's answer
2020-11-19T17:54:10-0500

xˉ=2.112 lb,s=1.111 lb\bar{x}=2.112\ lb, s=1.111\ lb

a. x=5.64 lbx=5.64\ lb


xxˉ=5.64 lb2.112 lb=3.528 lbx-\bar{x}=5.64\ lb-2.112\ lb=3.528\ lb


b.

xxˉs=3.528 lb1.111 lb3.1755\dfrac{x-\bar{x}}{s}=\dfrac{3.528\ lb}{1.111\ lb}\approx3.1755

The difference is approximately 3.1733  standard deviations.


c.


z=xxˉs31755z=\dfrac{x-\bar{x}}{s}\approx31755



d.Since 3.1755>2,3.1755>2, then the weight of 5.64 lb​ is significant.



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