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Answer on Statistics and Probability Question for jasmine

Question #840
A new Firestone tire is guaranteed to last for 40,000 miles. The actual mean life of the tires is 47,000 miles with a standard deviation of 4,000 miles.

a) What percent of the tires will last for at least 40,000 miles?
b) What percent of the tires will not last for at least 40,000 miles?
c) What is the probability that a tire will last for more than 50,000 miles?
d) The Firestone Company wants to advertise how long some of their tires last. They decide to state how long the top 3% of their tires will last. How many miles will the top 3% of their tires last?

Expert's answer
a) Let's find z - score:
z = (x-mu)/sigma = (40,000-47,000)/4,000 = - 1.75
p-value for z = 1.75 is 0.0401, for estimating the percent of the tires which last for at least 40,000 miles we have to consider right side of the distribution:
P(x > 40,000) = (1-P(x < 40,000))*100% = 95.99 %


b) the percent of the tires which are not last for at least 40,000 miles would be equal to P (x < 40,000) = 0.0401*100% = 4.01 %;
c) for more than 50,000 miles
z = (50,000-40,000)/4,000 = 2.5
the probability would be
P(x>50,000) = 00.62 %

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Comments

Assignment Expert
14.08.2012 08:58

Yes, you're absolutely right. Thanks for correcting us!

Melody
13.08.2012 13:32

Why, in answer c, is the z-score formula z=(50000-40000)/4000? Because the mean is 47000, should it be z=(50000-47000)/4000?

Assignment Expert
05.04.2012 07:36

Normal distribution with given mean and variance is considered for solving the problem. There are tables for normal distribution which give values of probability for different values of z. For example, take a look
<img 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" 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The standard normal distribution table provides the probability that random variable x is less than or equal to z. It does this for positive values of z only. So from given table we can find values of& P(x).
So values of p(x) are taken from the table of such kind.

Julian
03.04.2012 21:44

how do you know P (x>50,000) = .62%? I am very confused when it comes to the P (X) part

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