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 74 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean ? = 74 tons and standard deviation ? = 1.8 ton. What is the probability that one car chosen at random will have less than 73.5 tons of coal? (Round your answer to four decimal places.) What is the probability that 42 cars chosen at random will have a mean load weight x of less than 73.5 tons of coal? (Round your answer to four decimal places.)

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 74 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean ? = 74 tons and standard deviation ? = 1.8 ton. What is the probability that one car chosen at random will have less than 73.5 tons of coal? (Round your answer to four decimal places.) What is the probability that 42 cars chosen at random will have a mean load weight x of less than 73.5 tons of coal? (Round your answer to four decimal places.)

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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What is the probability that one car chosen at random will have less than 73.5 tons of coal? (Round your answer to four decimal places.)

What is the probability that 42 cars chosen at random will have a mean load weight x of less than 73.5 tons of coal? (Round your answer to four decimal places.)

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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