Answer:
(a) The difference between the highest weight and mean weight is 3.051 lb.
(b) The number of standard deviations is 2.77.
(c) The <em>z</em>-score of 5.26 is 2.77.
(d) The weight of 5.26 lb is significantly high.
Step-by-step explanation:
The random variable <em>X</em> is defined as the weights (lb) of plastic discarded by households.
The highest weight is,
The mean weight is, .
The standard deviation of the weight is, .
(a)
Compute the difference between the highest weight and mean weight as follows:
Thus, the difference between the highest weight and mean weight is 3.051 lb.
(b)
Compute the number of standard deviations the mean is from the maximum value as follows:
Thus, the number of standard deviations is 2.77.
(c)
The formula of <em>z</em>-score is:
Compute the <em>z</em>-score for <em>X</em> = 5.26 as follows:
Thus, the <em>z</em>-score of 5.26 is 2.77.
(d)
The <em>z</em>-scores between -2 and 2 are considered as neither significantly low nor significantly high.
The <em>z</em>-score for <em>X</em> = 5.26 is 2.77.
The value of <em>z</em> > 2.
Thus, the weight of 5.26 lb is significantly high.