A shipment of 6061-T6 aluminum is to be used in the manufacture of aircraft components. Federal regulations require that the material's mean tensile yield strength (sy) cannot be below 268 [MPa] or exceed 285 [MPa] within a 95% probability. 17 samples were machined from the available material and tested with the yield strength data given in the table below. Determine if the material meets the federal regulations. Also provide the range of values within which there is a 99% probability that the yield strength of a randomly tested selection of the material would fall.
Yield Strength (sy) [MPa]: 266.6615, 293.0881, 283.2358, 278.1679, 249.4136, 294.9664, 256.3751, 268.009, 282.8298, 293.061, 279.9604, 276.9924, 296.9422, 271.0592, 291.1144, 282.369, 271.4192