Respuesta :
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 z-score of 5.26 is 2.77.
(d) The weight of 5.26 lb is significantly high.
Step-by-step explanation:
The random variable X is defined as the weights (lb) of plastic discarded by households.
The highest weight is, [tex]X_{max.}=5.26\ lb[/tex]
The mean weight is, [tex]\bar x=2.209\ lb[/tex].
The standard deviation of the weight is, [tex]s=1.101\ lb[/tex].
(a)
Compute the difference between the highest weight and mean weight as follows:
[tex]X_{max.}-\bar x=5.26-2.209=3.051[/tex]
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:
[tex]Number\ of\ standard deviation=\frac{X_{max.}-\bar x}{s}=\frac{3.051}{1.0101}=2.77[/tex]
Thus, the number of standard deviations is 2.77.
(c)
The formula of z-score is:
[tex]z=\frac{X-\bar x}{s}[/tex]
Compute the z-score for X = 5.26 as follows:
[tex]z=\frac{X-\bar x}{s}=\frac{5.26-2.209}{1.101}=2.77[/tex]
Thus, the z-score of 5.26 is 2.77.
(d)
The z-scores between -2 and 2 are considered as neither significantly low nor significantly high.
The z-score for X = 5.26 is 2.77.
The value of z > 2.
Thus, the weight of 5.26 lb is significantly high.
