Question

a data set lists weights (lb) of plastic discarded by households. the highest weight is 5.49 lb, the mean of all of the weights is $overline{x}=1.914$ lb, and the standard deviation of the weights is $s = 1.409$ lb.
a. convert the weight of 5.49 lb to a z score.
b. 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 5.49 lb significant?
a. the z score is $z=square$.
(round to two decimal places as needed.)
b. the highest weight is

Explanation:

Step1: Use the z - score formula

The formula for the z - score is \(z=\frac{x-\bar{x}}{s}\), where \(x = 5.49\) (the data value), \(\bar{x}=1.914\) (the mean), and \(s = 1.409\) (the standard deviation).

$$z=\frac{5.49 - 1.914}{1.409}$$

Step2: Calculate the numerator

\(5.49-1.914=3.576\)
So, \(z=\frac{3.576}{1.409}\)

Step3: Calculate the z - score

\(z=\frac{3.576}{1.409}\approx2.54\)

Step4: Determine significance for part (b)

We know that if \(z\) is between \(- 2\) and \(2\), the value is not significant. Since \(z = 2.54>2\)

Answer:

a. The \(z\) - score is \(z = 2.54\)
b. The highest weight is significantly high.