4. Automatic Loader 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 of 75 tons and standard deviation of 0.8 ton. (a) State N~ ( , ) (b) What is the probability that one car chosen at random will have less than 74.5 tons of coal? (c) What is the probability that 20 cars chosen at random will have a mean load weight ? of less than 74.5 tons of coal?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
4. Automatic Loader 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
deviation of 0.8 ton.
(a) State N~ ( , )
(b) What is the probability that one car chosen at random will have less than 74.5 tons of coal?
(c) What is the probability that 20 cars chosen at random will have a mean load weight ? of less than 74.5
tons of coal?
Given:
The mean weights of coal loaded into each car is tons.
The standard deviation is ton.
Let X be a random variable that represents the actual weights of coal loaded into each car.
In the given scenario, the random variable X is normally distributed.
(a)
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