Central Limit Theorem The Tire Company manufactures tires that last a mean dista
ID: 3065256 • Letter: C
Question
Central Limit Theorem
The Tire Company manufactures tires that last a mean distance of 35,600 miles with a standard deviation of 4275 miles. The distances the tires last are normally distributed.
1. If a tire is randomly selected, what is the probability it lasts more than 35,000 miles?
2. Would it be unusual for a group of 40 randomly selected tires to last distances with a mean less than 35,000 miles?
3. Two customers file a complaint regarding Chemco. Customer A had a tire wear out after 35,000 miles. Customer B owns a fleet of 10 rental vehicles that use Chemco’s tires. The mean life of the rental fleet’s tires is less than 34,000 miles. Each vehicle in the fleet has 4 tires. Do either customers have a reasonable complaint? Explain.
4. The manufacturer wants to guarantee tires so that only 3% will have to be replaced before the number of guaranteed miles. For how many miles should the tires be guaranteed?
Explanation / Answer
1)
probability it lasts more than 35,000 miles:
2)
probability a group of 40 randomly selected tires to last distances with a mean less than 35,000 miles:
as probability of that happening is not less than 0.05 ; we can not claim that it is unusual
3)
probability of having 40 tires mean life less than 34000 miles:
as probability of that happening is very less ; threfore customer B has reasonable complaint.
4)
for 3 percentile ; z score =-1.8808
threfore corresponding distance =mean +z*std deviaiton =35600-1.8808*4275 =~27560 ( please try 27563 if this does not work due to rounding)_
for normal distribution z score =(X-)/ here mean= = 35600 std deviation == 4275.0000Related Questions
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