n/aMATH 2003-Z01 Fall 2020 Assignment 4 Name: Due on 09.27.20 Show all work clearly and in order to...

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n/aMATH 2003-Z01 Fall 2020 Assignment 4 Name: Due on 09.27.20 Show all work clearly and in order to receive full credit. Circle or otherwise indicate your final answers. Justify your answers algebraically whenever possible. Submit your completed assign- ment as either a .doc, .docx, or .pdf format file. No late work will be accepted. You don’t have to type your solutions. You can just take pictures of your hand-written solutions and convert them into PDF. 1. If all values in a data set are the same, then the sample variance is equal to . 2. For a bell-shaped data set, approximately of the data will be in the interval µ− σ to µ+ σ. 3. Chebyshev’s Inequality states that for any data set, the proportion of data within k standard deviations of the mean is at least . 4. The following are the weights, in pounds, for samples of offensive and defensive linemen in the National Football league. Offense: 335 301 307 252 260 307 325 310 305 305 264 325 Defense: 284 290 286 355 305 295 297 325 310 297 314 348 (a) Find the sample variance and standard deviation for the weights for the offensive linemen. (b) Find the sample variance and standard deviation for the weights for the defensive linemen. (c) Is there greater spread in the weights of the offensive or defensive linemen? 5. In a recent survey of 655 working Americans ages 25-34, the average weekly amount spent on lunch was $44.60 with standard deviation $2.81. The weekly amounts are approximately bell-shaped. (a) Estimate the percentage of amounts that are between $36.17 and $53.03 (b) Estimate the percentage of amounts that are between $41.79 and $47.41. (c) Between what two values will approximately 95% of the amounts be?

Gajula Nagasai · Accepted Answer

1.If all the values in the data set are the same, then the sample variance is equal to Zero
The following is the proof 
The formula for the sample variance is defined as 
               
The following table explains the calculation of sample variance with same values in the data set
	x
	(x – x bar)
	(x-x bar)2
	12
	0
	0
	12
	0
	0
	12
	0
	0
	12
	0
	0
	12
	0
	0
	12
	0
	0
	12
	0
	0
	12
	0
	0
	12
	0
	0
	12
	0
	0
	12
	0
	0
	12
	0
	0
	X bar =12
	∑ (x – x bar) = 0
	∑ (x-x bar)2 = 0
From the above calculation, we have ∑ (x-x bar)2 = 0 and n-1 = 11
Then, Sample variance = 0/11 = 0
Therefore, if all the values in the data set are the same, then the sample variance is equal to Zero
3. For a bell-shaped data set, approximately 68% of data set values will be in the interval μ – σ to μ + σ.
Example we have the average students of weight in a school is 45 kg with Standard deviation 5 kg. Then,
Lower control limit μ – σ = 45 -5 = 40 kg
Upper control limit μ + σ = 45 + 5 =50 kg 
The above control limits are called as one sigma control limits.
(μ – σ, μ + σ) = (40, 50)
Therefore 68% of student’s weight of in a school will fall within the range of 40 kg to 50 kg.
 2. Chebyshev’s Inequality states that for any data set,

MATH 2003-Z01 Fall 2020 Assignment 4 Name: Due on XXXXXXXXXX Show all work clearly and in order to receive full credit. Circle or otherwise indicate your final answers. Justify your answers...

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