Question

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 hopper car loader is set to put 62 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean μ = 62 tons and standard deviation σ = 0.9 ton.

(a) What is the probability that one car chosen at random will have less than 61.5 tons of coal? (Round your answer to four decimal places.)

(b) What is the probability that 17 cars chosen at random will have a mean load weight x of less than 61.5 tons of coal? (Round your answer to four decimal places.)

Answer 1

Given data

Population mean weight in tons of coal

Population standard daviation

(a) Now given that one sample is chosen and we have to find the probablity of geting the weight less than 61.5 tone

so X=61.5

now lets find Z score first

Now from the standard probablity distribution table the area under the Z= -0.56 will be the probablity of getting the weight less than 61.5 tone

so

(b) Now given that

number of car chosen (n)=17

and we have to find the probablity of getting the avarege of the sample less than 61.5 tone

so lets

Now lets find Z score first

Now from the standard probablity distribution table the area under the Z= -2.29 will be the probablity of getting the average weight less than 61.5 tone

so