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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MATH 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?