Question

A cenposry peoduces steel rods. The lengrhs of the steel roda are nomally distobuted wth ames of 179 3-cn and a standasd deviation of 2 1 crs. For shipmest, 12 steel rods are bandled together Find the pesbability that he aveage ength of a andornly selected bondle of steel rods is betwees 1774-cn and i9 4m Exter you answer as a oumber accueate to 4 decinal places Atavers obtained usng exactzcoes az-sceres sounded to 3 decinal places ae acepted

Answer 1

Solution :

Given that mean µ = 179.3 , standard deviation = 2.1 , n = 12

=> P(177.4 < M < 179.4) = P((177.4 - 179.3)/(2.1/sqrt(12)) < (x - µ)/(σ/sqrt(n)) < (179.4 - 179.3)/(2.1/sqrt(12)))

= P(-3.134 < Z < 0.165)

= 0.5666