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ravenconner85
05.03.2020 •
Mathematics
A major television manufacturer has determined that its 44 inch screens have a mean service life that can be modeled by a normal distribution with a mean of 6 years and a standard deviation of one-half year (6 months). What is the probability that the service life of that product is between 5 and 7 years
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Ответ:
And we can find this probability with thie difference:
And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:
Where
and ![\sigma=0.5](/tpl/images/0534/3150/41db0.png)
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability with thie difference:
And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.
Ответ:
Idk my guy try this https://www.tiger-algebra.com/en/
Step-by-step explanation:
it works