Anybody up???? If so can someone help me with my math please?

A soft drink machine outputs a mean of 25 ounces per cup. The machine's output is normally distributed with a standard deviation

Alla [95]

Answer:

The probability of filling a cup between 18 and 33 ounces is 0.93719.

Step-by-step explanation:

The variable here is the machine's output which is normally distributed.

The normal distribution is defined by two parameters, namely, the mean and the standard deviation.

The population mean for this normal distribution is $\\ \mu = 25$ ounces per cup, and a population standard deviation of $\\ \sigma = 4$ ounces (per cup).

To solve this question, we can use the standard normal distribution (which has a mean = 0, and a standard deviation = 1). All we have to do is to "transform" those raw scores into z-scores, and then consult a standard normal table (available in every Statistics book or on the Internet).

Roughly speaking, the z-scores are values that tell us the distance from the mean in standard deviations units. For positive values of it, the value is above the mean, and negative values tell us that the value is below the mean.

We can obtain the z-scores using the next formula:

$\\ z = \frac{x - \mu}{\sigma}$ [1]

Where

z is the z-score.

x is the raw score.

$\\ \mu$ is the population mean.

$\\ \sigma$ is the population standard deviation.

The probability of filling a cup between 18 and 33 ounces

Having all the information above, we can proceed as follows:

First Step: obtaining the z-score for 18 to find the corresponding probability of this value in this normal distribution.

Using the formula [1], we have:

$\\ z = \frac{18 - 25}{4}$

$\\ z = \frac{-7}{4}$

$\\ z = -1.75$

This tells us that the value is below the mean and is -1.75 standard units from it.

Most of the standard normal tables are made for positive values of z. However, since the normal distribution is symmetrical around the mean, we, fortunately, can obtain the corresponding probability considering that:

$\\ P(z$

Then, consulting the cumulative standard normal table for z = 1.75, we have that the corresponding cumulative probability is $\\ P(z$ .

Thus

$\\ P(z1.75)$

Then, the probability is $\\ P(z$

We have to remember that this is the standardized value for x = 18, and for this normal distribution (mean = 25, standard deviation = 4), it has the same cumulative probability [P(x<18) = 0.04006].

Second Step: obtaining the z-score for 33 to find the corresponding probability of this value in this normal distribution.

We can proceed in the same way to obtain the z-score and the associated probability with the raw score x = 33. We can see that this value is above the mean (positive).

$\\ z = \frac{33 - 25}{4}$

$\\ z = \frac{8}{4}$

$\\ z = 2$

The raw score is two (2) standard deviations above the mean. The corresponding cumulative probability is (consulting the standard normal table):

$\\ P(z$

Then the cumulative probability for $\\ P(z$ . We have to remember that this is the standardized value for x = 33, and for this normal distribution, it has the same cumulative probability [P(x<33) = 0.97725].

Third step: subtract both values and we obtain "the probability of filling a cup between 18 and 33 ounces", that is:

$\\ P(18 < x < 33) = 0.97725 - 0.04006$

$\\ P(18 < x < 33) = 0.93719$

Thus, the probability of filling a cup between 18 and 33 ounces is 0.93719.

We can see the area that represents this in the graph below.

6 0

4 years ago

Hello! PLEASE SOLVE ALL 4 ASAP! YOU WILL BE A GREAT HELP! :)

LiRa [457]

Answer:

1. a+b 2.a-b. 3. ab 4. a/b

8 0

3 years ago

Read 2 more answers

Determine whether each pair of figures is similar. Justify your answer

damaskus [11]

They are correspondent but we’re missing a little bit of the answer, it’s one of the first 2 though. A or B, can’t tell though.

3 0

3 years ago

3(n+11)-5n=-2(n-12)+9

eduard

Simplifying
3(n + 11) + -5n = -2(n + -12) + 9
Reorder the terms:
3(11 + n) + -5n = -2(n + -12) + 9
(11 * 3 + n * 3) + -5n = -2(n + -12) + 9
(33 + 3n) + -5n = -2(n + -12) + 9
Combine like terms: 3n + -5n = -2n
33 + -2n = -2(n + -12) + 9
Reorder the terms:
33 + -2n = -2(-12 + n) + 9
33 + -2n = (-12 * -2 + n * -2) + 9
33 + -2n = (24 + -2n) + 9
Reorder the terms:
33 + -2n = 24 + 9 + -2n
Combine like terms: 24 + 9 = 33
33 + -2n = 33 + -2n
Add '-33' to each side of the equation.
33 + -33 + -2n = 33 + -33 + -2nCombine like terms: 33 + -33 = 0
0 + -2n = 33 + -33 + -2n
-2n = 33 + -33 + -2n
Combine like terms: 33 + -33 = 0
-2n = 0 + -2n
-2n = -2n
Add '2n' to each side of the equation.
-2n + 2n = -2n + 2n
Combine like terms: -2n + 2n = 0
0 = -2n + 2n
Combine like terms: -2n + 2n = 0
0 = 0
Solving
0 = 0
Couldn't find a variable to solve for.
This equation is an identity, all real numbers are solutions.

4 0

3 years ago

For several hours you watch a group playing dice on the street and you notice that the owner of the dice often wins.

Nostrana [21]

Answer:

there is no question

Step-by-step explanation:

It looks like the owner plays dirty, meaning he uses a trick of some kind to somehow influence the outcome in such a way, that it's outcome is no longer random.

By influencing the outcome, the owner can obtain an advantage over the playeers who are not aware of the trick or skill involved.

This is unfair and can be considered "dirty". This game is 'fixed'.

4 0

4 years ago