A data set lists weights (lb) of plastic discarded by households. The highest weight is 5.65 lb, the mean of all of the weights is x=2.135 lb, and the standard deviation of the weights is s=2.316 lb. a. What is the difference between the weight of 5.65 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 5.65 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 5.65 lb significant?

Explained below.

Step-by-step explanation:

Let the random variable X represent the weights (lb) of plastic discarded by households.

It is provided that the mean weight is, and the standard deviation of the weights is, .

(a)

Compute the difference between the weight of 5.65 lb and the mean of the weights as follows:

Thus, the difference is 3.515 lb.

(b)

Compute the number of standard deviations as follows:

Thus, the number of standard deviation is 1.518.

(c)

Compute the z-score for the weight 5.65 lb as follows:

Thus, the z-score is 1.52.

(d)

The z-score for the weight 5.65 lb is 1.52.

This  z-score lies in the range -2 and 2.

Thus, the weight of 5.65 lb is neither significantly low nor significantly high.

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: