Question

Question content area top

Part 1
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?
Question content area bottom
Part 1
a. The difference is 2.7852.785 lb.
​(Type an integer or a decimal. Do not​ round.)
Part 2
b. The difference is enter your response here standard deviations.
​(Round to two decimal places as​ needed.)

Answer 1

The difference between the weight of 5.12 lb and the mean weight is 2.785 lb.

Explanation:

To find the difference between the highest weight and the mean weight, we simply subtract the mean from the highest weight:

5.12 lb - 2.335 lb = 2.785 lb

Therefore, the difference between the weight of 5.12 lb and the mean weight is 2.785 lb.

Part 2

b. Answer: The difference between the weight of 5.12 lb and the mean weight is 1.71 standard deviations.

Explanation: To find the number of standard deviations that the difference in weight represents, we divide the difference by the standard deviation:

2.785 lb / 1.631 lb = 1.71

Therefore, the difference between the weight of 5.12 lb and the mean weight is 1.71 standard deviations.