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gunnatvinson
11.02.2020 •
Mathematics
Toms of Maine sells toothpaste in a tube advertised to contain 8 ounces. In their continuous production process, the amount of toothpaste put in a tube is normally distributed with a mean of 8.21 ounces and a standard deviation of 0.09 ounces. If the actual capacity of the tubes used is 8.45 ounces, what proportion of the tubes will be filled beyond capacity?
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Ответ:
And we can find this probability using the z table or excel:
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 amount of toothpasye of a population, and for this case we know the distribution for X is given by:
Where
and ![\sigma=0.09](/tpl/images/0506/6890/ec584.png)
The capacity is 8.45 ounces and 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 using the z table or excel:
Ответ:
hypotenuse =
=
= 26mi