Question

In: Statistics and Probability

The average number of miles (in thousands) that a car's tire will function before needing replacement...

The average number of miles (in thousands) that a car's tire will function before needing replacement is 66 and the standard deviation is 11. Suppose that 43 randomly selected tires are tested. Round all answers to 4 decimal places where possible and assume a normal distribution.

  1. What is the distribution of X? X ~ N
  2. What is the distribution of ¯x? ¯x ~ N
  3. If a randomly selected individual tire is tested, find the probability that the number of miles (in thousands) before it will need replacement is between 65.6 and 66.7.
  4. For the 43 tires tested, find the probability that the average miles (in thousands) before need of replacement is between 65.6 and 66.7.
  5. For part d), is the assumption that the distribution is normal necessary?  

Solutions

Expert Solution

orchestra answered 2 years ago
Next > < Previous

Related Solutions

The average number of miles (in thousands) that a car's tire will function before needing replacement...
The average number of miles (in thousands) that a car's tire will function before needing replacement is 66 and the standard deviation is 14. Suppose that 18 randomly selected tires are tested. Round all answers to 4 decimal places where possible and assume a normal distribution. What is the distribution of XX? XX ~ N(,) What is the distribution of ¯xx¯? ¯xx¯ ~ N(,) If a randomly selected individual tire is tested, find the probability that the number of miles...
1. A tire company produces a tire that has an average life span of 500 miles...
1. A tire company produces a tire that has an average life span of 500 miles with a standard deviation of 250. The distribution of the life spans of the tires is normal. What is the probability that the tires lasts between 530 and 375 miles? (Round three decimal places) 2. A tire company produces a tire that has an average life span of 480 miles with a standard deviation of 30. The distribution of the life spans of the...
1)  Average tire life is 30,000 miles (μ = 30,000) and σ = 2,300 miles.  What is the...
1)  Average tire life is 30,000 miles (μ = 30,000) and σ = 2,300 miles.  What is the      probability that a tire will last 35,000 miles (or more)? 2)  If μ = 130 and σ = 20 on an employment test and the company only hires from the top      75% of scores, what is the lowest score you can get and still get hired? 3)  The SAT has μ = 500 and σ = 100.  What score would put you in the top 15%? 4)  For...
A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before...
A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past studies of this tire, the standard deviation is known to be 8,000. A survey of owners of that tire design is conducted. From the 28 tires surveyed, the mean lifespan was 46,500 miles with a standard deviation of 9,800 miles. Using alpha = 0.05, is the data highly inconsistent with the claim? Find the 95% confidence interval...
A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before...
A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past studies of this tire, the standard deviation is known to be 8000. A survey of owners of that tire design is conducted. From the 28 tires surveyed, the mean lifespan was 46,500 miles with a standard deviation of 9800 miles. Do the data support the claim at the 5% level?
A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before...
A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past studies of this tire, the standard deviation is known to be 8,000. A survey of owners of that tire design is conducted. From the 28 tires surveyed, the mean lifespan was 46,500 miles with a standard deviation of 9,800 miles. Using a confidence level of 95%, is the data highly inconsistent with the claim?
A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before...
A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past studies of this tire, the standard deviation is known to be 8,000. A survey of owners of that tire design is conducted. Of the 28 tires surveyed, the mean lifespan was 46,500 miles with a standard deviation of 9,800 miles. Using alpha = 0.05, is the data highly consistent with the claim? Note: If you are using...
A tire company claims that the lifetimes of its tires average 49750 miles. The standard deviation...
A tire company claims that the lifetimes of its tires average 49750 miles. The standard deviation of tire lifetimes is known to be 4750 miles. You sample 75 tires and will test the hypothesis that the mean tire lifetime is at least 49750 miles against the alternative that it is less. Assume, in fact, that the true mean lifetime is 49250 miles. It is decided to reject H0 if the sample mean is less than 49150. Find the level and...
A tire manufacturer claims its tires will last for 80,000 miles on average when properly maintained....
A tire manufacturer claims its tires will last for 80,000 miles on average when properly maintained. To investigate this claim, a retail tire store has surveyed 49 recent customers of that particular tire and determined those tires lasted for an average of 77,470 miles. The population standard deviation is known to be 7,700 miles. Compute the value of the appropriate test statistic to test this claim. Enter your answer as a decimal rounded to two places. Indicate a negative value...
A tire manufacturer has been producing tires with an average life expectancy of 26,000 miles. Now...
A tire manufacturer has been producing tires with an average life expectancy of 26,000 miles. Now the company is advertising that its new tires' life expectancy has increased. In order to test the legitimacy of the advertising campaign, an independent testing agency tested a sample of 6 of their tires and has provided the following data. Ho: m < 26 Ha: m > 26 Life Expectancy (In Thousands of Miles) 28 27 25 28 29 25 At 99% confidence, what...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT