Mathematics, 16.04.2020 02:10, christianconklin22

A machine fills containers with a particular product. Assume the filling weights are normally distributed with a variance of 0.81 ounces2. If 85% of the containers hold greater than 20 ounces, find the machine's mean filling weight (in ounces).

a. 19.0640
b. 19.1576
c. 20.8424
d. None of the answers is correct
e. 20.9360

Answers: 1

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Answers

answered: sillslola816oxb5h7

P(X 20) =0.85

And by the complement rule we know P(X

We need to find a z score value that accumulates 0.15 of the area on the left and 0.85 of the area on the right and we got:

z = -1.036

Since P(Z and now using the z score formula we have this:

$-1.03643 = \frac{20 -\mu}{0.9}$

And solving for the mean we got:

$\mu = 20 + 1.03643 *0.9 = 20.93$

So the best anwer for this case would be:

e. 20.9360

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 weights of a population, and for this case we know the distribution for X is given by:

$X \sim N(\mu,\sqrt{0.81}=0.9)$

Where $\mu$ the mean and $\sigma=0.9$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

We know the following condition:

P(X 20) =0.85

And by the complement rule we know P(X

We need to find a z score value that accumulates 0.15 of the area on the left and 0.85 of the area on the right and we got:

z = -1.036

Since P(Z and now using the z score formula we have this:

$-1.03643 = \frac{20 -\mu}{0.9}$

And solving for the mean we got:

$\mu = 20 + 1.03643 *0.9 = 20.93$

So the best anwer for this case would be:

e. 20.9360

answered: Guest

3 is greater then both of those numbers

answered: Guest

the correct answer is a) "catholic church".

the proposals that liberals in mexico made during 1855 were particularly focused on a person's individual rights, such as the freedom of speech, the freedom of conscience, freedom of assembly, and the right to possess weapons.

when the constitution was formally published 2 years later (1857). it also contained an article which permitted education free from any religious influence, the removal of the catholic church institutional privileges, and the sale of property belonging to the church. all of these provisions were clearly against the catholic church interests.