Arrrange the numbers in increasing order. 14.204 14.200 14.240 14.210
1 answer:
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Answer:
Therefore there's a 99.99% probability the motherboard of your new computer will last for at least 15 years.
Step-by-step explanation:
This is the general idea to solve the problem.
Suppose that the mean and variance of the your distribution are . respectively. Then, according to the problem you are looking for the probability.
Consider then the following random variable.
Using the central limit theorem distribution will be close to normal, and its mean and variance will be
, respectively. Therefore you just have to find the probability that a normally distributed random variable with that mean and that variance which I just mentioned is less than 14.
For this case we have that
Then you have that
and we have that if is a normally distributed random variables with mean 280 and variance 70 we have that
the actual probability we are looking for is
Therefore there's a 99.99% probability the motherboard of your new computer will last for at least 15 years.