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 actual weight of coal loaded into each car are normally distributed with a mean of 75 tons and a standard deviation of 0.8 tons.  Let  be the average coal weight of a random sample of 20 cars.

1. Calculate the mean and the standard deviation of , and describe the shape of its sampling distribution.
2. What is the probability that the mean coal weight of the random sample of 20 cars is less than 74.5 tons?

Answer 1

Solution :

Given that ,

mean =   = 75

standard deviation = = 0.8

n = 20

mean = = 75

standard deviation= =  / n = 0.8/ 20=0.1789

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

= P(z < -2.79)

Using z table  

= 0.0026   

probability=0.0026