Question

1. (1) 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?

2. (2) Suppose we are interested in finding a 95% confidence interval for the mean SAT Verbal score of students at a certain high school. Five students are sampled, and their SAT Verbal scores are

   560, 500, 470, 660, 640.
   (a) Find the mean and standard deviation of this sample. You may use R.

   (b) Find a 95% confidence interval for the mean SAT Verbal scores.

Answer 1