Question

A data set lists weights​ (lb) of plastic discarded by households. The highest weight is 5.12 ​lb, the mean of all of the weights is x=2.335 ​lb, and the standard deviation of the weights is s=1.631 lb.

a. What is the difference between the weight of 5.12 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 5.12 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 5.12 lb​ significant?


Need help on c

Answer 1

The weight of 5.12 lb has a z-score of 1.708

Explanation:

To convert the weight of 5.12 lb to a z-score, we first need to find the deviation from the mean:

z = (x - μ) / σ

where x is the weight of 5.12 lb, μ is the mean of all weights, and σ is the standard deviation of the weights.

z = (5.12 - 2.335) / 1.631

z = 1.708

Therefore, the weight of 5.12 lb has a z-score of 1.708.