If you wanna be Dora then please help me!

4- A manufacturing process produces items whose weights are normally distributed. It is known that 22.57% of all the items produ

galben [10]

Answer:

$\\ \mu = 118\;grams\;and\;\sigma=30\;grams$

Step-by-step explanation:

We need to use z-scores and a standard normal table to find the values that corresponds to the probabilities given, and then to solve a system of equations to find $\\ \mu\;and\;\sigma$ .

<h3>First Case: items from 100 grams to the mean</h3>

For finding probabilities that corresponds to z-scores, we are going to use here a <u>Standard Normal Table </u><u><em>for cumulative probabilities from the mean </em></u><em>(Standard normal table. Cumulative from the mean (0 to Z), 2020, in Wikipedia) </em>that is, the "probability that a statistic is between 0 (the mean) and Z".

A value of a z-score for the probability P(100<x<mean) = 22.57% = 0.2257 corresponds to a value of z-score = 0.6, that is, the value is 0.6 standard deviations from the mean. Since this value is <em>below the mean</em> ("the items produced weigh between 100 grams up to the mean"), then the z-score is negative.

Then

$\\ z = -0.6\;and\;z = \frac{x-\mu}{\sigma}$

$\\ -0.6 = \frac{100-\mu}{\sigma}$ (1)

<h3>Second Case: items from the mean up to 190 grams</h3>

We can apply the same procedure as before. A value of a z-score for the probability P(mean<x<190) = 49.18% = 0.4918 corresponds to a value of z-score = 2.4, which is positive since it is after the mean.

Then

$\\ z =2.4\;and\; z = \frac{x-\mu}{\sigma}$

$\\ 2.4 = \frac{190-\mu}{\sigma}$ (2)

<h3>Solving a system of equations for values of the mean and standard deviation</h3>

Having equations (1) and (2), we can form a system of two equations and two unknowns values:

$\\ -0.6 = \frac{100-\mu}{\sigma}$ (1)

$\\ 2.4 = \frac{190-\mu}{\sigma}$ (2)

Rearranging these two equations:

$\\ -0.6*\sigma = 100-\mu$ (1)

$\\ 2.4*\sigma = 190-\mu$ (2)

To solve this system of equations, we can multiply (1) by -1, and them sum the two resulting equation:

$\\ 0.6*\sigma = -100+\mu$ (1)

$\\ 2.4*\sigma = 190-\mu$ (2)

Summing both equations, we obtain the following equation:

$\\ 3.0*\sigma = 90$

Then

$\\ \sigma = \frac{90}{3.0} = 30$

To find the value of the mean, we need to substitute the value obtained for the standard deviation in equation (2):

$\\ 2.4*30 = 190-\mu$ (2)

$\\ 2.4*30 - 190 = -\mu$

$\\ -2.4*30 + 190 = \mu$

$\\ \mu = 118$

7 0

3 years ago

What is 6 to the 2nd power ÷ 2(3)+4

butalik [34]

$6^2:2(3)+4=36:2(3)+4=18(3)+4=54+4=\huge\boxed{58}$

5 0

3 years ago

ILL GIVE BRAINLIEST IF YOU GET IT RIGHT AND EXPLAIN

koban [17]

Answer:

y = 2

x = 50

Step-by-step explanation:

We can first find y by doing 12y+5 = 18y-7 since vertical angles are always congruent.

We want to combine like terms so we subtract 12y from both sides (what you do on one side needs to be done to the other) and we get 5 = 6y-7 and now we add 7 to both sides to get 12 = 6y.

Like I said we did this because we combine like terms!!!

Now we want to isolate the y and we do this by dividing 6 from both sides which lets us get 2 = y

Now that we know what y is we can plug it into any of the equations using y.

I plugged it into the top right equation cause it was easier.

12(2)+5

24+5

29!

That angle is 29!

Now that we know that we can begin solving for x.

The equation that has x + 29 make 180 degrees because it is a straight line so we use this to solve for x!

3x+1+29=180 (We want to start combining like terms now)

3x+30=180(Subtract 30 from both sides)

3x=150 (Isolate the x by dividing 3 from both sides)

x=50!

We can prove this is right by inserting x into it's expression. That tells us the angle is 151. Now we add 151+151+29+29 and we get 360!

4 0

3 years ago

A game at the state fair has a circular target with a radius of 10.7 cm on a square board measuring 30 cm on a side. Players win

Stells [14]

Answer:

The probability of hitting the circular area = P(H) = favorable area/ total area = Area of the circle / Area of the square

Step-by-step explanation:

= π/9

6 0

3 years ago

Which of the following statements is not true

Aloiza [94]

Answer:

The slope of AB is different from the slope of BC is NOT TRUE.

Step-by-step explanation:

AB and BC are on the same straight line, so their slopes are the same.

6 0

2 years ago