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 weight of coal loaded into each car is normally distributed, with mean of 75 tons and standard deviation of 0.8 ton.(a) There are 97% of the cars will be loaded with more than K tons of coal. What is the value of K?(b) What is the probability that one car chosen at random will have less than 74.4 tons of coal?(c) Among 20 randomly chosen cars, what is the probability that more than 2 cars will be loaded with less than 74.4 tons of coal?

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Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section: Chapter Questions

Problem 22SGR

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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 weight of coal loaded into each car is normally distributed, with mean of 75 tons and standard deviation of 0.8 ton.

(a) There are 97% of the cars will be loaded with more than K tons of coal. What is the value of K?
(b) What is the probability that one car chosen at random will have less than 74.4 tons of coal?
(c) Among 20 randomly chosen cars, what is the probability that more than 2 cars will be loaded with less than 74.4 tons of coal?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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