Question

3. Coal is carried from a mine in West Virginia to a power plant in New York in hopper Cars on a long train. The automatic hoppe ong train. The automatic hopper car loader is set to put 75 tons of coal ar. The actual weights of coal loaded into each car are normally distributed with mean u = 75tons and standard deviation o=0.8tons What is the probability that one car chosen at random will have less than 74.5 tons of coal? b) What is the probability that 20 chosen at random will have a mean load weight of less than 74.5 tons of coal? c) Suppose the weight of coal in one car was less than 74.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? d) Suppose the weight of coal in 20 cars selected at random had an average less than 74 5 tons. Would that fact make you suspect that the loader had slipped out of adjustment (4 pts each)

Answer 1

Soluhion:- 6=0.8 5) P(ze 74.5-75, a) P(xc74.5) Plze X- 0.8 -P(z<-0.62) 0.2676 b) Plăc7 4.5) = Z< 74.5-75 018 :P1zc-2.80) 0. 0026 No Because it is quite usual tobser ve () weiglh Car to be less thon 79.5s tons. jon me obse we to dy it is unwsual lus Because mean yes to be less Jh on 74.5 weiget of 20 Car