The question is: A major tire manufacturer advertises that their highest quality radial tire has a distribution of wear that is mound-shaped with a mean of 60,000 miles and a standard deviation of 6,000 miles. Assume their advertisement is true.
The questions are:
Approximately, what percentage of the company's best radial tires will travel between 42,000 miles and 78,000 miles before wearing out?
Approximately what percentage of the company's best radial tires will travel more than 72,000 miles before wearing out?
I need help finding those answers - Any help is appreciated.
2007-06-05 09:22:19 · 1 answers · asked by Zach M 2 in Education & Reference ➔ Homework Help
Conveniently, the the range for which the problem is stated is exactly plus and minus three standard deviations (60000 - 3*6000 to 60000 + 3*6000).
And we know (don't we?) that 99.7% of a normal distribution lies between -3 std dev and +3 std dev. So there's your first answer. Just look it up in a table of normal distribution.
The second part asks what fraction of the distribution exceeds +2 std dev. Again, simply refer to a table of normal distribution and you find that 2.27% of the tires should be expected to exceed 72000 miles.
This is one of those things that you don't calculate unless you have a calculator with the function already built in. Just look it up in a table. You might want to memorize the values for 1, 2, and 3 std dev
2007-06-05 09:43:39 · answer #1 · answered by dogsafire 7 · 0⤊ 0⤋