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Professor, Perelman School of Medicine at the University of Pennsylvania The correlation coefficient for the (normal score spasms 14 year old beagle rumalaya forte 30 pills online, original [untransformed] data) pairs is back spasms 8 weeks pregnant buy discount rumalaya forte 30 pills on-line. The plot for the transformed data is clearly more linear in appearance than the plot for the original data muscle relaxant 114 buy cheapest rumalaya forte. Occasionally, a particular transformation can be dictated by some theoretical argument, but often this is not the case and you may wish to try several different transformations to find one that is satisfactory. Other investigators in this field had previously used all three of the transformations illustrated. Number of cases Sperm concentrations (106/ml) (a) (b) Number of cases Sperm concentrations (106/ml) (c) (d) Figure 7. Engineering : 153­159) reported the following data on bearing load life (in millions of revolutions); the corresponding normal scores are also given: x Normal Score x Normal Score 7. Based on the plot, do you think it is reasonable to assume that the normal distribution provides an adequate description of the steam rate distribution? Observation 1800 + 1500 1200 900 * * * + * * * * + * - * + - +-+-+-+-+-+ * -1. Observation + * + * + * * * + * * * * * - +-+-+-+-+-+ Construct a normal probability plot. Do the sample data suggest that the cadmium concentration distribution is not normal? Construct a normal probability plot, and comment on the plausibility of a normal distribution as a model for component lifetime. The 12 smallest scores result from placing a negative sign in front of each of the given nonzero scores. The square-root transformation was used to obtain a distribution of values that was more symmetric Video solution available Data set available online but not required 7. Another power transformation that has been suggested by meteorologists is the cube root: transformed value (original value)1/3. The original values and their cube roots (the transformed values) are given in the following table: Original Transformed Original Transformed was recorded for each yarn sample. The resulting data are given in the following table: 86 76 180 196 597 497 188 239 135 193 146 264 198 90 246 182 568 236 169 175 251 15 38 229 211 423 55 277 157 220 653 364 20 166 180 185 244 143 224 149 98 195 61 38 93 338 20 198 65 151 249 262 121 337 571 290 284 264 315 353 400 88 282 341 124 398 93 105 229 400 292 264 180 40 279 71 396 203 55 61 131 42 325 40 81 246 203 124 286 194 176 321 250 135 186 185 829 137 350 188 0. Construct a frequency distribution using the class intervals 0 to 100, 100 to 200, and so on. Find a transformation for these data that results in a more symmetric histogram than what you obtained in Part (b). The investigators conducted their research using a national sample of 2071 households and recorded the number of toothpaste purchases for each household participating in the study. The results are given in the following frequency distribution: Number of Purchases Number of Households (Frequency) Construct a histogram of the transformed data. Which of the cube-root and square-root transformations appear to result in the more symmetric histogram(s)? Construct a relative frequency distribution for this data set, and draw the corresponding histogram. The number of cycles of strain to breakage Bold exercises answered in back 10 to 20 to 30 to 40 to 50 to 60 to 70 to 80 to 90 to 100 to 110 to 120 to 130 to 140 to 150 to 160 to 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 904 500 258 167 94 56 26 20 13 9 7 6 6 3 0 2 Data set available online but not required Video solution available 424 Chapter 7 Random Variables and Probability Distributions a. Does the square-root transformation result in a histogram that is more symmetric than that of the original data? Draw a histogram based on class intervals 5 to 10, 10 to 15, 15 to 20, 20 to 25, 25 to 30, 30 to 40, 40 to 50, 50 to 100, and 100 to 500. Use a calculator or statistical computer package to calculate logarithms of these observations, and construct a histogram. Consider transformed value and 1original value construct a histogram of the transformed data. A large number of topsoil samples were analyzed for manganese (Mn), zinc (Zn), and copper (Cu), and the resulting data were summarized using histograms. The investigators transformed each data set using logarithms in an effort to obtain more symmetric distributions of values. Using the Normal Distribution to Approximate a Discrete Distribution the distribution of many random variables can be approximated by a carefully chosen normal distribution. In this section, we show how probabilities for some discrete random variables can be approximated using a normal curve.   