The distance travelled by cars with automatic tranmissions before they develop transmission problems is, on average, 21,600 km with a standard deviation of 4275km. A car dealership claims that their automatic cars will last up to 18,000 km before developing transmission problems. Assume that this variable is normally distributed.
1) Are the dealership's claims reasonable? Explain.
2) What proportion of with automatic transmissions would develop transmission problems within 13,500km?
2007-08-07 06:07:40 · 2 answers · asked by Anonymous in Education & Reference ➔ Homework Help
Assuming a normal distribution, that means that 99% of all vehicles will fall within + or - 3 standard deviations from the mean. Therefore, given the numbers you have 99% of all vehicles will fall between 21,600 +or- 3(4275)km. That is:
21600 +or- 12825 or 8775 to 34425km.
Within one standard deviation is (17,325 to 25,825km) and, based on a normal distribution, this likelihood is 68% that one falls within that range. So, I would say the dealer's claims are reasonable given that they are on the low side of the mean and within one standard deviation.
The proportion of cars that would develop transmission problems within 13,500 is more difficult. If you actually meant within 13,050 then it would be within 2 standard deviations and would be 1/2 of 95% (the total number of cars to fall within 2 SD's on BOTH sides of the mean. That would be 47.5%.
2007-08-07 06:20:42 · answer #1 · answered by jurydoc 7 · 2⤊ 0⤋
I would help you, but sorry math is just not my subject. Good luck on finding your answer.
2007-08-07 06:11:29 · answer #2 · answered by tiafromtijuana 4 · 1⤊ 1⤋