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 73 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean ? = 73 tons and standard deviation ? = 0.6 ton. What is the probability that 40 cars chosen at random will have a mean load weight x of less than 72.5 tons of coal?

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 73 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean ? = 73 tons and standard deviation ? = 0.6 ton. What is the probability that 40 cars chosen at random will have a mean load weight x of less than 72.5 tons of coal?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

Can the standard deviation of a data set be zero?
A standardized exam's scores are normally distributed. In a recent year, the mean test score was 1457 and the standard deviation was 315. The test scores of four students selected at random are 1900, 1200, 2180, and 1350. Find the z-scores that correspond to each value and determine whether any of the values are unusual. The is the z-score for 1900?
The playing life of a Sunshine radio has a Normal distribution with a mean of 600 hours and a standard deviation of 100 hours. What percent of the time would you expect a radio to last no more than 600 hours?
The heights of all women in the United States are known to be normally distributed with a mean of 63 inches and standard deviation of 3 inches. The U.S. Navy requires that fighter pilots have heights between 58 inches and 72 inches. Find the percentage of women in the United States that meet this height requirement. Round the solution to two decimal places, if necessary.
Each students in a local school district write a national examination. The average on this year national exam is 150 with a standard deviation of 20. Schools where the overall average is between 1.5 and 3.0 standard deviations above the mean are eligible for additional funding. What is the average range a school must achieve to be eligible for funding?
The length of songs in the Big Hair playlist of a Statistics professor's mp3 player varies from song to song. This variation can be modeled by the normal distribution, with a mean song length of �=4.3 minutes and a standard deviation of �=0.65 minutes. (Note that a song that has a length of 4.5 minutes is a song that lasts for 4 minutes and 30 seconds.)The professor decides to shuffle the playlist, which means that the mp3 player will randomly pick a song within this particular playlist and play it next.(a) What is the probability that the next song to be played is between 3.9 and 4.85 minutes long? Answer to four decimals. (b) What proportion of all the songs in this playlist are longer than 5 minutes? Use four decimals in your answer. (c) 20% of all the songs in this playlist are at most how long, in minutes? Enter your answer to two decimals. minutes(d) There are 247 songs in the Big Hair playlist. How many of these would you expect to be longer than 5 minutes in length? Use two…
A student takes a test in his math course and scores 45 points and a test in his psychology courseand scores 71 points. Scores on each test were normally distributed. On the math test the classhas a mean of 40 and a standard deviation of 15. On the psychology test the class has a mean of 75and a standard deviation of 10. On which test did the student do better?
A standardized exam's scores are normally distributed. In a recent year, the mean test score was 1549 and the standard deviation was 318. The test scores of four students selected at random are 1960,1270, 2250, and 1450. Find the z-scores that correspond to each value and determine whether any of the values are unusual.
Entry to a certain University is determined by a national test. The scores on this test are normally distributed with a mean of 500 and a standard deviation of 100. Tom wants to be admitted to this university and he knows that he must score better than at least 80% of the students who took the test. Tom takes the test and scores 595. Will he be admitted to this university?
Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation 20. Find Upper P 4 which is the IQ score separating the bottom 44% from the top 96%.
A particular fruit's weights are normally distributed, with a mean of 342 grams and a standard deviation of 14 grams.The heaviest 2% of fruits weigh more than how many grams?Give your answer to the nearest gram.
218 234 210 | 261 | 265 175 191 | 308 253 295 253 | 220 | 234 | 232 189 208 190 202 159 | 304 275 | 305 308 295