The average fuel efficiency of U.S. light vehicles (cars, SUVs, minivans, vans, and light trucks) for 2005 was 21 miles per gallon (mpg). If the standard deviation of the population was 2.8 and the gas ratings were normally distributed, (a) what is the probability that the fuel used for a random sample of 25 light vehicles is under 18? (b) between 20 and 24?

The average fuel efficiency of U.S. light vehicles (cars, SUVs, minivans, vans, and light trucks) for 2005 was 21 miles per gallon (mpg). If the standard deviation of the population was 2.8 and the gas ratings were normally distributed, (a) what is the probability that the fuel used for a random sample of 25 light vehicles is under 18? (b) between 20 and 24?

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...

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The average fuel efficiency of U.S. light vehicles (cars, SUVs, minivans, vans, and light trucks) for 2005 was 21 miles per gallon (mpg). If the standard deviation of the population was 2.8 and the gas ratings were normally distributed, (a) what is the probability that the mean mpg for a random sample of 25 light vehicles is under 18? (b) between 20 and 24?
Fran is training for her first marathon, and she wants to know if there is a significant difference between the mean number of miles run each week by group runners and individual runners who are training for marathons. She interviews 42 randomly selected people who train in groups and finds that they run a mean of 47.1 miles per week. Assume that the population standard deviation for group runners is known to be 4.4 miles per week. She also interviews a random sample of 47 people who train on their own and finds that they run a mean of 48.5 miles per week. Assume that the population standard deviation for people who run by themselves is 1.8 miles per week. Test the claim at the 0.01 level of significance. Let group runners training for marathons be Population 1 and let individual runners training for marathons be Population 2. Step 2 of 3 : Compute the value of the test statistic. Round your answer to two decimal places.
Show neat and complete solution. (... The average fuel efficiency of U.S. light vehicles (cars, SUVs, minivans, vans, and light trucks) for 2005 was 21 miles per gallon (mpg). If the standard deviation of the population was 2.8 and the gas ratings were normally distributed, (a) what is the probability that the mean mpg for a random sample of 25 light vehicles is under 18? (b) between 20 and 24? Given: Required: Solution: a. b.
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 65 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean ? = 65 tons and standard deviation ? = 1.7 ton. (a) What is the probability that one car chosen at random will have less than 64.5 tons of coal? (Round your answer to four decimal places.)(b) What is the probability that 37 cars chosen at random will have a mean load weight x of less than 64.5 tons of coal? (Round your answer to four decimal places.)
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For the midterm exam in science of grade 8 students, the mean grade is 82 with standard deviation of 13. A random sample of size 30 will be taken. a. What is the probability that the sample mean is less than 75? b. What is the probability that the sample mean is greater than 90?
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 90 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean ? = 90 tons and standard deviation ? = 1.1 ton. (a) What is the probability that one car chosen at random will have less than 89.5 tons of coal? (Round your answer to four decimal places.)(b) What is the probability that 39 cars chosen at random will have a mean load weight x of less than 89.5 tons of coal? (Round your answer to four decimal places.)
In the class of 2019, more than 1.6 million students took the SAT. The distribution of scores on the math section (out of 800) is approximately normal with a mean of 528 and standard deviation of 117. What proportion of students earned scores between 500 and 600 on the SAT math test?
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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 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 ? = 1.9 ton. (a) 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.)(b) What is the probability that 50 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 69 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean ? = 69 tons and standard deviation ? = 1.5 ton. (a) What is the probability that one car chosen at random will have less than 68.5 tons of coal? (Round your answer to four decimal places.)(b) What is the probability that 46 cars chosen at random will have a mean load weight x of less than 68.5 tons of coal? (Round your answer to four decimal places.)(c) Suppose the weight of coal in one car was less than 68.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? YesNo Suppose the weight of coal in 46 cars selected at random had an average x of less than 68.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? Why? Yes, the probability that this…