23. In a study of warp breakage during the weaving of fabric

(Technometrics, 1982: 63), 100 specimens of yarn were tested. The number of cycles of strain to breakage was determined for each yarn specimen, resulting in the following data:

86 146 251 653 98 249 400 292 131 169 175 176 76 264 15 364 195 262 88 264 157 220 42 321 180 198 38 20 61 121 282 224 149 180 325 250 196 90 229 166 38 337 65 151 341 40 40 135 597 246 211 180 93 315 353 571 124 279 81 186 497 182 423 185 229 400 338 290 398 71 246 185 188 568 55 55 61 244 20 284 393 396 203 829 239 236 286 194 277 143 198 264 105 203 124 137 135 350 193 188

a. Construct a relative frequency histogram based on the class intervals 0–100, 100–200, . . . , and comment on features of the histogram.

b. Construct a histogram based on the following class intervals: 0–50, 50–100, 100–150, 150–200, 200–300, 300–400, 400–500, 500–600, and 600–900.

c. If weaving specifications require a breaking strength of at least 100 cycles, what proportion of the yarn specimens in this sample would be considered satisfactory?