#2) A vendor measures the weights, in kilograms (kg), of a sample of packages sh
ID: 3042513 • Letter: #
Question
#2) A vendor measures the weights, in kilograms (kg), of a sample of packages she sends out. The sample mean is 10 kg and the sample standard deviation is 2 kg. The descriptive statistics for this exercise are shown below. Variable Weights Weights 2.2 Weights 2.20.1 9 0 22.10 9 0 10.000 0.666 2.00 6.400 8.550 10.100 2.100 12.300 9 0 22.00 1.47 4.40 14.08 18.81 22.22 26.62 27.06 27.16 1.47 4.40 14.18 18.9 22.32 26.72 She converts the sample mean and sample standard deviation to pounds by multiplying by 2.2. What is the sample mean (in pounds)? What is the standard deviation (in pounds)? How have the mearn and standard deviation changed from the original mean and standard deviation? The vendor decides to use a heavier packaging, which increases the weight of each package by 0.1 pounds. Now, what is the sample mean and sample standard deviation (in pounds)? How have the mean and standard deviation changed from the answers in (a)? a) b)Explanation / Answer
Part (a)
Sample mean = 2.2 x 10 = 22 pounds Answer 1
Sample standard deviation = 2.2 x 2 = 4.4 pounds Answer 2
When each observation is multiplied by a constant, both mean and standard deviation get multiplied by that constant. ANSWER 3
Part (a)
Sample mean = (2.2 x 10) + 0.1= 22.1 pounds Answer 1
Sample standard deviation = 2.2 x 2 = 4.4 pounds Answer 2
When a constant is added (implication of increasing the weight of each package by 0.1 pound) to each observation, the mean is increased by that constant, but standard deviation does not undergo any change. ANSWER 3
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.