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 75 tons of coal into
each car. The actual weights of coal loaded into each car are normally distributed, with
mean μ = 75 tons and standard deviation σ = 0.8 ton.

(a) 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 cars chosen at random will have a mean load weight
of less than 74.5 tons of coal?

Answer 1

Solution :

Given that ,

mean = = 75

standard deviation = = 0.8

a)

P(x < 74.5) = P((x - ) / < (74.5 - 75) / 0.8)

= P(z < -0.63)

= 0.2643 Using standard normal table,

Probability = 0.2643

b)

n = 20

= = 75 and

= / n = 0.8 / 20 = 0.1789

P( < 74.5) =   P(( - ) / < (74.5 - 75) / 0.1789)

= P(z < -2.79)   Using standard normal table.   

Probability = 0.0026