Question

a data set lists weights (lb) of plastic discarded by households. the highest weight is 5.69 lb, the mean of all of the weights is \\( \overline { x } = 2.016 \\) lb, and the standard deviation of the weights \\( s = 1.966 \\) lb.

a. what is the difference between the weight of 5.69 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 5.69 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 5.69 lb significant?

a. the difference is 3.674 lb.
(type an integer or a decimal. do not round.)
b. the difference is 1.87 standard deviations.
(round to two decimal places as needed.)
c. the z score is \\( z = \square \\).
(round to two decimal places as needed.)

Explanation:

Step1: Recall the formula for z - score

The formula for the z - score is \(z=\frac{x-\bar{x}}{s}\), where \(x\) is the data value, \(\bar{x}\) is the mean, and \(s\) is the standard deviation.
We know from part (a) that \(x - \bar{x}=3.674\) (the difference between the value \(x = 5.69\) and the mean \(\bar{x}=2.016\)), and \(s = 1.966\) (the standard deviation).

Step2: Calculate the z - score

Substitute the values into the z - score formula: \(z=\frac{x-\bar{x}}{s}\).
\(z=\frac{3.674}{1.966}\)
\(z\approx1.87\)

Answer:

\(1.87\)