## [answered] Batch 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

An engineer is trying to determine the suitability of two metal alloys (alloy A and alloy B) in fabricating industrial machinery fuse elements - the part of the fuse which melts after reaching a certain temperature or current. Samples are taken from batches of alloys and are subjected to laboratory test where the melting temperatures are recorded. The melting temperatures for both alloys are provided in the excel file. The engineer had asked your help describing the extremely high and extremely low melting temperatures of the alloys by using G-I plot for minima and maxima. (for all numeric questions, please specify your answers in one decimal places of accuracy, ###.# - format, using standard convention in rounding of values)

For alloy A, what is the plotting position v for the largest of the minimal values?

For Alloy A, what is the plotting position v for the largest of the maximal values?

What is the asymptotic distribution of the minimal melting temperature of alloy A?

What is the asymptotic distribution of the maximal melting temperature of alloy A?

For alloy B, what is the plotting position v for the largest of the minimal values?

For alloy B, what is the plotting position v for the largest of the maximal values?

What is the asymptotic distribution of the minimal melting temperature of alloy B?

What is the asymptotic distribution of the maximal melting temperature of alloy B?

Batch

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47

48

49 sample 1 sample 2 sample 3 sample 4 sample 5

258.8

144.6

264.2

151.7

164.3

158.6

168.6

280.0

154.7

169.3

217.9

216.8

203.6

163.1

177.8

241.0

227.3

249.6

246.8

144.4

167.3

243.7

141.6

108.3

114.6

215.9

168.6

277.4

269.5

138.4

189.3

195.0

179.5

254.4

202.5

205.4

276.6

167.4

169.6

199.9

191.0

233.4

224.5

127.0

190.0

172.5

140.9

177.1

184.0

285.2

262.0

206.5

215.9

176.9

166.1

294.6

131.8

230.6

250.1

226.3

154.9

229.7

301.9

156.5

165.2

191.8

200.8

202.7

199.2

166.6

154.9

155.4

214.3

191.7

169.6

177.7

172.7

182.5

185.4

126.8

232.6

180.5

198.0

136.7

170.7

183.3

166.0

257.9

110.3

226.0

161.7

195.3

260.3

195.5

235.6

175.2

301.2

205.6

201.0

144.7

188.8

150.5

158.5

143.3

232.3

181.5

214.0

268.4

185.4

265.3

181.6

131.8

144.5

220.1

245.2

198.0

238.2

187.5

133.6

373.1

267.7

155.3

258.3

105.2

150.6

222.9

225.4

179.4

168.2

251.7

166.9

183.2

186.3

193.1

233.8

143.0

187.0

153.5

156.3

191.9

225.2

309.9

188.5

198.8

131.9

179.1

186.0

153.8

125.0

244.7

286.9

270.7

181.0

153.3

158.5

153.4

134.5

130.1

235.4

183.7

175.3

194.8

208.8

294.9

248.9

269.4

199.7

253.0

223.4

224.5

209.3

209.0

175.8

182.5

229.5

250.6

164.2

205.1

172.2

220.1

164.3

258.2

212.2

135.2

145.6

205.5

180.0

185.2

246.5

194.6

168.0

153.2

156.5

181.7

218.5

232.6

226.3

226.3

169.8

154.4

155.8

200.0

209.6

214.3

135.2

168.1

271.7

154.8

149.5

224.6

317.9

140.7

181.3

224.1

158.1

258.0

216.0

179.0

100.6

156.1

184.8

164.1

294.9

141.0

225.8

151.9

156.0

248.6

220.1

220.8

156.7

312.2

193.3

204.2

192.0

264.9

169.9

248.9

275.9

150.9

258.4

174.9

225.0

194.1

203.6 50

51

52

53

54

55

56

57

58

59

60 173.1

216.0

163.7

170.7

217.3

203.3

218.7

135.3

157.7

214.7

247.1 171.6

180.1

194.9

250.1

196.2

249.1

168.7

149.5

188.1

204.4

186.7 237.9

214.6

253.5

192.7

128.9

262.1

151.3

234.2

229.7

176.3

273.2 223.2

209.9

163.8

161.9

194.7

240.0

130.5

115.7

104.2

193.2

248.2 227.9

163.4

187.6

170.4

171.0

202.1

181.1

173.1

253.1

217.9

160.9 Batch

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53 sample 1 sample 2 sample 3 sample 4 sample 5

252.3

243.9

174.3

210.9

192.4

266.7

196.0

56.0

187.8

236.7

278.9

59.3

219.5

187.0

198.5

206.9

196.6

97.5

129.4

181.0

160.8

212.2

287.5

125.9

308.7

196.0

201.1

198.3

189.4

204.1

154.3

341.8

115.8

196.5

159.8

153.3

215.0

153.1

290.6

168.9

132.1

253.4

252.9

247.6

112.8

203.1

286.5

123.1

223.2

284.6

113.3

241.6

230.0

184.8

235.7

213.9

143.5

240.7

133.9

275.2

152.8

250.4

244.5

179.7

268.4

221.8

167.7

199.6

246.5

243.3

172.3

168.0

302.1

154.4

302.3

366.3

209.2

208.2

235.1

210.2

246.8

242.9

233.3

273.3

207.9

112.0

251.7

173.4

260.1

207.7

274.8

256.5

159.2

174.9

280.2

202.7

275.1

115.1

233.7

150.6

177.3

203.3

288.8

256.6

176.5

223.1

157.0

146.1

182.3

266.7

206.2

211.9

198.9

239.0

184.9

197.2

203.9

230.4

250.1

234.0

160.4

185.0

235.0

203.6

172.1

242.1

185.8

218.6

262.9

181.0

149.0

201.3

244.4

135.9

196.9

208.1

191.3

208.2

260.4

162.4

122.1

184.7

222.2

166.9

259.9

159.4

138.0

199.5

134.1

152.8

252.8

207.1

222.2

165.5

191.3

193.7

315.1

133.0

276.0

187.3

182.3

224.3

136.2

202.0

233.0

313.9

264.1

310.7

177.5

219.7

182.3

290.4

127.7

213.3

175.9

179.7

216.3

159.5

207.9

154.7

192.7

174.8

210.9

169.6

201.9

171.2

311.0

205.7

263.3

251.5

127.8

185.4

148.0

239.0

214.9

227.8

195.4

214.6

202.0

222.8

248.9

122.1

189.2

260.4

228.2

240.6

224.4

157.7

149.0

206.3

244.0

256.8

180.7

256.3

171.2

251.2

276.6

299.5

285.5

147.2

217.1

207.1

278.1

248.8

246.3

170.0

194.6

231.8

243.4

160.3

292.0

185.7

237.4

148.0

272.2

238.5

245.9

199.3

129.9

271.0

175.8

192.5

224.0

208.1

176.0

259.6

226.3

228.7

228.4

151.5

223.9

240.8

273.0

191.2

226.8

215.5

170.6

276.9

175.9

213.6

181.6

275.4

231.3

134.9

324.9 54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80 161.9

232.0

236.3

159.9

279.7

225.2

119.2

220.2

173.5

196.8

277.8

198.3

162.5

201.8

186.5

230.3

197.7

106.2

277.4

203.6

146.0

144.5

201.7

171.4

194.1

201.7

222.7 224.5

197.5

273.7

211.7

137.8

92.2

111.9

150.1

263.1

120.0

248.2

262.3

230.0

194.7

187.4

120.7

196.2

251.8

250.3

268.1

154.1

222.9

206.1

168.9

308.6

207.5

196.5 251.3

209.5

247.4

298.2

191.8

158.2

246.8

228.6

229.1

219.9

143.6

211.6

75.7

270.2

188.4

204.0

164.2

210.6

147.7

238.0

157.6

188.1

155.9

97.6

206.5

69.3

259.6 162.1

286.9

198.5

258.3

250.2

242.3

221.2

194.2

158.1

220.8

235.4

238.0

127.3

155.3

256.3

166.7

172.9

293.8

199.1

281.7

229.8

236.4

269.6

228.0

233.2

234.3

192.5 174.0

237.3

171.1

130.3

189.2

211.2

290.0

235.8

219.2

177.3

175.0

125.9

277.2

208.7

199.3

131.5

231.5

289.6

277.3

247.3

263.2

250.3

190.3

85.3

176.2

261.8

170.9

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