Question

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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?
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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

Answer: The difference of 2.785 lb is approximately 1.702 standard deviations away from the mean.

Step-by-step explanation: The difference between the weight of 5.12 lb and the mean of the weights is:

5.12 - 2.335 = 2.785 lb

To find how many standard deviations this is, we can use the formula:

z = (x - mu) / sigma

where z is the z-score, x is the weight, mu is the mean, and sigma is the standard deviation.

Plugging in the values, we get:

z = (5.12 - 2.335) / 1.631

z ≈ 1.702

Therefore, the difference of 2.785 lb is approximately 1.702 standard deviations away from the mean.