Question

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 70 and the standard deviation is 10. Suppose that 46 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 71.8 and 72.9.
  4. For the 46 tires tested, find the probability that the average miles (in thousands) before need of replacement is between 71.8 and 72.9.
  5. For part d), is the assumption that the distribution is normal necessary? Yes or No

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Life of a tire follows normal distribution with a mean of 60,000 miles with standard deviation...
Life of a tire follows normal distribution with a mean of 60,000 miles with standard deviation of 5000 miles. A tire of the same kind is randomly selected. Find the probability that the tire will last (a) more than 52,000 miles (b) less than 68,000 but more than 52,000 miles (c) more than 68,000 miles.
Please answer all three parts and show all work. Thank you! A cheap tire is said...
Please answer all three parts and show all work. Thank you! A cheap tire is said to have its tire wear (how long it lasts (in thousands of miles as N(30,12) (that is normal with μ =30, σ =12) Find the probability that 1. A tire last between 29,000 and 33,000 miles 2. 40% of tires last less than how many miles? 3. 45% of tires last more than how many miles?
The tires sold at Best Tires last an average of 80,000 miles with a standard deviation...
The tires sold at Best Tires last an average of 80,000 miles with a standard deviation of 12,000 miles. Let LaTeX: \bar{x}x ¯ be the average number of miles a sample of 4 randomly selected tires purchased from Best Tires will last. According to the Central Limit Theorem, what is the standard deviation of the sampling distribution of x ¯ ? Group of answer choices 3,000 48,000 6,000 12,000
The average amount of money that people spend at Don Mcalds fast food place is $7.7000...
The average amount of money that people spend at Don Mcalds fast food place is $7.7000 with a standard deviation of $1.8900. 46 customers are randomly selected. Please answer the following questions, and 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(,) What is the distribution of ∑x∑x? ∑x∑x ~ N(,) What is the probability that one...
  The lifetime of a tire can be represented by a normal distribution with an average of...
  The lifetime of a tire can be represented by a normal distribution with an average of 35,000 kilometers and a standard deviation of 4,000 kilometers. Find the probability that the time of a tire is more than 30,000 kilometers. Find the value of K such that the probability that the life time of a tire is less than K is 0.95. A sample of 80,000 was taken from these tires. Approximately how many have a life time greater than 38,000...
Consumer Reports indicated that the average life of a refridgerator before replacement is mean= 14 years...
Consumer Reports indicated that the average life of a refridgerator before replacement is mean= 14 years with a (95% of data) range from 9 to 19 years. Let x= age at which refrigerator is replaced. Assume that x has a distribution that is approximately normal. a) Find a good approximation for the standard deviation of x values. b) What is the probability that someone will keep a refrigerator fewer than 11 years before replacement? c) What is the probability that...
Consumer Reports indicated that the average life of a refrigerator before replacement is 14 years with...
Consumer Reports indicated that the average life of a refrigerator before replacement is 14 years with a (95% of data) range from 9 to 19 years. Let x = age at which a refrigerator is replaced. Assume that x has a distribution that is approximately normal. a. Find a good approximation for the standard deviation of x values. b. What is the probability that someone will keep a refrigerator fewer than 11 years before replacement? c. What is the probability...
The average production cost for major movies is 59 million dollars and the standard deviation is...
The average production cost for major movies is 59 million dollars and the standard deviation is 21 million dollars. Assume the production cost distribution is normal. Suppose that 13 randomly selected major movies are researched. Answer the following questions. Round all answers to 4 decimal places where possible. What is the distribution of X ? X ~ N( , ) What is the distribution of ¯ x ? ¯ x ~ N( , ) For a single randomly selected movie,...
The average production cost for major movies is 69 million dollars and the standard deviation is...
The average production cost for major movies is 69 million dollars and the standard deviation is 19 million dollars. Assume the production cost distribution is normal. Suppose that 8 randomly selected major movies are researched. Answer the following questions. Give your answers in millions of dollars, not dollars. Round all answers to 4 decimal places where possible. What is the distribution of X ? X ~ N( , ) What is the distribution of ¯ x ? ¯ x ~...
The average production cost for major movies is 66 million dollars and the standard deviation is...
The average production cost for major movies is 66 million dollars and the standard deviation is 19 million dollars. Assume the production cost distribution is normal. Suppose that 17 randomly selected major movies are researched. Answer the following questions. Give your answers in millions of dollars, not dollars. Round all answers to 4 decimal places where possible. What is the distribution of X X ? X X ~ N(,) What is the distribution of ¯ x x¯ ? ¯ x...