please do from b to f and show steps 2. A quality control inspector for a produc
ID: 3040949 • Letter: P
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please do from b to f and show steps
2. A quality control inspector for a production process has obtained measurements on the length (in cm) of 30 randomly selected dowels from the process in order to check whether the process is producing acceptable dowels. The measurements are in the column dowels in the excel file "Assignment 1 data" on Culearn. a Construct a stem-and-leaf plot for the dowel data (graph, stem-and-leaf) What is the median dowel length? b What are the smallest and largest dowel lengths? c) Two thirds of the dowel lengths are below what value? d) What fraction of the dowel lengths is below 5.5 cm? e) Circle which one of the following statements would best fit this data? and the mean and median are approximately equal the mean is much greater than the median the mean is much smaller than the median f) For this data would you use the Empirical Rule or Chebychev's Theorem? Why?Explanation / Answer
Mean=Ex/n=163.86/30=5.462
Median=n+1/2=31/2=15.5th value i.e. (5.44+5.46)/2=5.45
To calculate 2/3rd of dowel lengths, percentile*n=0.6733*30=20.199 value i.e. 20th value i.e. 5.55
Dowels 5.07 5.1 5.26 5.27 5.29 5.29 5.3 5.34 5.34 5.35 5.36 5.39 5.4 5.42 5.44 5.46 5.47 5.5 5.53 5.55 5.57 5.58 5.61 5.62 5.63 5.65 5.68 5.75 5.79 5.85 5.07 Min (Smallest) b 5.85 Max (Largest) b 5.55 2/3rd of dowel lengths are below this value c 5.462 Mean e 5.45 Median e the mean and median are approximately equal e 0.566666666666667 or 17/30 observations below 5.5 Fraction of data below 5.5 d Here, we should be using Chebyshev's Theorem because it applies to all datasets whereas empirical rule applies to only bell curved (normal distribution) datasets. This is not a bell curved dataset. fRelated Questions
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