A data set list weight (lb) of plastic discarded by household. The highest weight of 5.67 lb the mean of all of the weight is x = 2.142lb. And the standard deviation of the weight is s=2.311lb.What is the difference between the weight of 5.67 and the mean of the weight. B. How many standards deviation is that the difference found in part (a). C. Convert the weight of 5.67 to a Z score.
A. The difference between the weight of 5.67 lb and the mean of the weight (x = 2.142 lb) is:
5.67 - 2.142 = 3.528 lb.
B. To find how many standard deviations the difference in part (a) is, we divide the difference by the standard deviation:
3.528 / 2.311 ≈ 1.526.
So, the difference is approximately 1.526 standard deviations.
C. To convert the weight of 5.67 lb to a Z score, we use the formula:
Z = (x - μ) / σ
where Z is the z-score, x is the weight, μ is the mean, and σ is the standard deviation.
Z = (5.67 - 2.142) / 2.311
Z = 3.528 / 2.311
Z ≈ 1.526.
So, the Z-score for the weight of 5.67 lb is approximately 1.526.