Coal in West Virginia

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 65 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean μ = 65 tons and standard deviation σ = 1.5 ton.

(a) What is the probability that one car chosen at random will have less than 64.5 tons of coal? (Round your answer to four decimal places.)

Answer 1

We want to find P(X<64.5) Since X (the weight of coal in a car) is normally distributed with μ = 65 tons and standard deviation σ = 1.5 ton, we can convert X into z by using z=(x-μ)/σ formula, so we can use the normal table

Z=(64.5-65)/1.5=-0.5/1.5=-0.3333.. approximately equal to -0.33

P(X<64.5)=P(Z<-0.33)=0.3707 as we an see from the table.( Find -0.3 on the z column on the left draw an imaginary line to the right and then find 0.03 on the top and draw an imaginary line downward and find where the two lines meet?