A bottling company uses a filling machine to fill plastic bottles with cola. The bottles are supposed are supposed to contain 300m. In fact, the contents vary according to a Normal Distribution with mean of 298 mL and a standard deviation of 3 mL. (a) What is the probability that an individual bottle contains less than 295 mL? Show your work. (b) What is the probability that the mean contents of six randomly chosen bottles is less than 295 mL? Show your work.

Answers

Answer 1

Answer:

0.15866 ; 0.0071627

Step-by-step explanation:

Given that:

Mean (m) = 298

Standard deviation (s) = 3

A.) P(x < 295)

Using the relation to obtain the standardized score (Z) :

Z = (x - m) / s

Z = (295 - 298) / 3 = - 1

p(Z < - 1) = 0.15866 ( Z probability calculator)

B.)

Z = (x - m) / s /sqrt(n)

Z = (295 - 298) / 3/sqrt(6) = −2.449489

p(Z < - 2.449) = 0.0071627 ( Z probability calculator)

Answer 2
The probability will be:(a) 0.15866(b) 0.007163

Given values are:

Mean,

m = 298

Standard deviation,

s = 3

(a)

P(x < 295)

The standardized score will be:

→ [tex]Z = \frac{(x-m)}{s}[/tex]

By substituting the values, we get

      [tex]= \frac{(295-298)}{3}[/tex]

      [tex]= \frac{-3}{3}[/tex]

      [tex]= -1[/tex]

Now,

By using the Z probability calculator, we get

→ [tex]p(Z< -1) = 0.15866[/tex]

(b)

The standardized score will be:

→ [tex]Z = \frac{x-m}{\frac{s}{\sqrt{n} } }[/tex]

By putting the values,

      [tex]= \frac{295-298}{\frac{3}{\sqrt{6} } }[/tex]

      [tex]= -2.449489[/tex]

Now,

→ [tex]p(Z < -2.449)= 0.007163[/tex]

Thus the responses above are correct.

Learn more about probability here:

https://brainly.com/question/20369155


Related Questions

Please help meeeee :,(

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Answer:

I pretty sure the answer is ASA, I hope it's right!

write the factored form of the polynomial.

P(x) = x4 – 7x3 + 13x2 + 3x – 18

Answers

Answer:

(x+1)(x-2)(x-3)^2

Step-by-step explanation:

Sorry, mate. That math is too hard to type out online. You's guys will just have to take my word for it!

what is the quotient of -0.05 ÷ (-5/8)​

Answers

Answer:

-0.08 YW <3

Step-by-step explanation:

Answer:

0.08

Step-by-step explanation:

Use a calculator!

pls helppppppppppppp

Answers

Answer:

B is the answer

Step-by-step explanation:

Part A) 8*25=200 less 2x15= $170

Part B 3*25 = $75 less 6x15= $90- Total loss $15 (75-90)

etc

how long does it take for a car driving at 0.92 per minute to drive at 7.4

Answers

ANSWER : ABOUT 8 MINUTES

0.92 * 8 = 7.36
takes 8 minutes to get to 7.4

I need this ASAP!!! Please

Answers

the answer is 5/8 or 0.625

I REALLY NEED HELP!! Determine whether the graph represents a proportional relationship. (4 points)

A graph is shown. The x-axis is labeled from 0 to 9. The y-axis is labeled from 0 to 15. Four points are shown on the graph on ordered pairs 0, 2 and 1, 6 and 2, 10 and 3, 12. These points are joined by a line. The label on the x-axis is Number of cars. The title on the y-axis is Number of wheels.

a
Yes, it is a proportional relationship because the graph goes through the origin

b
Yes, it is a proportional relationship because the graph is a straight line

c
No, it is not a proportional relationship because the graph is not a straight line

d
No, it is not a proportional relationship because the graph does not go through the origin

Answers

Answer:

d) No, it is not a proportional relationship because the graph does not go through the origin

Step-by-step explanation:

A proportional relationship has to pass through the origin (0,0)

What is the area of a rectangle with a length of 3 ft and a width of 16.1 ft? 48.3 ft2 38.2 ft2 24.15 ft2 19.1 ft2

Answers

Vent fmtsmstjqrjatjwtnatnatn

plzzzz helppp im stupid!!!

Answers

Answer:

1. A'B'C'

(2, 4) (4, 10) (14, 2)

A''B''C'' (2, 8) (8, 14) (14, 6)

2. D'E'F'G

(-6, 3) (-9, 3) (-6, 12) (-9, 12)

D''E''F''G'' (-2, 1) (-3, 1) (-2, 4) (-3, 4)

Step-by-step explanation:

Ok. So, when you are dialating, you first step is to determine wether it is bigger or smaller. If the scale factor is more than one, it is an enlargment or getting bigger. If it is less than 1, it is a reduction and getting smaller. Then, it is just math. Lets say that the point is (2, 4) and your scale factor is 2. Multiply 2 times 2 to get 4. Then multiply 4 times 2 to get 8. Your new cordinante is (4, 8).

You are not stupid you can do it!

6. Find how long it takes $600 to double if it is invested at 12%
interest compounded monthly.
With work

Answers

Answer:

A = $697.09

Step-by-step explanation:

A = P (1 + r/n)

A = 600 (1 + 0.05/365)

A = $697.09

(Giving Brainlyst)
Awnser this with the letter and fraction listed
EX. H- 2/3
Thanks!

Answers

Answer:

C-7/8

R-8/9

P-61/66

L-11/18

I-3/4

A-7/12

O-47/55

H-29/40

S-28/33

T-4/5

M-11/12

E-71/84

U-13/42

N-19/20

I swear to god if I don’t get brainliest I’m going to lose it I haven’t done this math in like four years and it kinda took a while.... but I hope it helped u ☺️☺️☺️❤️❤️❤️❤️

Step-by-step explanation:

Answer:

I-9/12 or 3/4

T- 8/10 or 4/5

C- 7/8

A- 7/12

M- 11/12

R- 7/9

O- 36/55

E- 71/84

P- 61/66

H- 29/40

U- 13/42

L- 11/18

S- 28/33

N- 19/20

Step-by-step explanation:

if any are wrong, just lmk and i'll see what I did. But, i'm pretty sure they're right

In‌ ‌a‌ ‌survey‌ ‌of‌ ‌100‌ ‌dog‌ ‌owners,‌ ‌75%‌ ‌said‌ ‌that‌ ‌they‌ ‌always‌ ‌feed‌ ‌their‌ ‌dog‌ ‌dry‌ ‌food.‌ ‌
What‌ ‌fraction‌ ‌of‌ ‌the‌ ‌dog‌ ‌owners‌ ‌surveyed‌ ‌feed‌ ‌their‌ ‌dog‌ ‌dry‌ ‌food?‌

Answers

Answer:

3/4

Step-by-step explanation:

Please give brainliest!

Miguel has 48 pieces of quartz. He wants to
divide the pieces equally into 9 bags. How
many pieces of quartz will be in each bag?
How many pieces will be left over? Use tiles
or draw an array to help you find the answer.

Answers

Answer:

49

Step-by-step explanation:

12 men can dig a pond in 8 days. How many men can dig it in 6 days?

Answers

Answer:

It would be 16 men.

Step-by-step explanation:

Let the number of men dig a pond in 6 day be x. Then,

It is a case of inverse variation.

12 × 8 = 6x

=> 96 = 6x

=> x = 96/6

=> x = 16

Hence, 16 men can dig a pond in 6 days.

Answer:

Answer is 16…..

12 men take 8 days for digging a pond, so we use simple method to solve this problem.

We multiple the both things that is 12 and 8 then get 96 is the result which is equal to multiple of 6 days and ?Men then get 16 men

Step-by-step explanation:

I literally put it on the comments lol

A line has a slope of 3, is increasing, and passes through the point (2,7). What is its y-intercept?

Answers

The y-intercept is 1.

First, we need to put this into point slope form which is y-7=3(x-2)

Next, multiply using the distributive property. y-7=3x-6

Lastly, we want to get y by itself so add 7 on both sides. y=3x+1.

Using the slope intercept form, y=mx+b where b is the y-intercept, we can see that the line will cross the y-axis at 1.

Hope this helps✨❤️

The y-intercept of the line is 1

Using the slope - intercept relation :

y = bx + cc = Intercept; b = slope point (2,7)

Substituting the values into the relation :

7 = 3(2) + c

7 = 6 + c

c = 7 - 6

c = 1

Therefore, the y-intercept of the line is 1.

Learn more on Intercept:https://brainly.com/question/25987747

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Need help on 1, 2, and 3. 50 points and brainliest

Answers

Answer:

1. 7/12

2. 6  2/5

3. 18/5

Step-by-step explanation:

Answer:

1st is 7/12

2nd is 6and 2/5

3rd is answer is not shown

Step-by-step explanation: Brainliest pls

hope this helped

A jar contains 5 blue marbles, 8 red marbles, 4 white marbles, and 3 purple marbles. Suppose you pick a marble at random without looking.

P(purple) =

Answers

Answer:

.15 or 15%

Step-by-step explanation:

5+8+4+3=20

3 purple marbles/20 total marbles= .15

What 3 consecutive numbers if the sum is 15333

Answers

Answer:

[tex]5110, 5111, 5112[/tex]

Step-by-step explanation:

Let [tex]x=[/tex] first consecutive number

[tex]x + (x+1)+(x+2) = 15333[/tex] ([tex]x[/tex] is the first number, [tex]x+1[/tex] would be the second consecutive number of the sequence, and [tex]x+2[/tex] would be the third)

[tex]3x + 3 = 15333[/tex]

[tex]3x = 15330[/tex]

[tex]x = 5110[/tex]

[tex]x+1 = 5110+1[/tex]

[tex]= 5111[/tex]

[tex]x+2 = 5110 + 2[/tex]

[tex]= 5112[/tex]

[tex]\therefore[/tex] the consecutive numbers that sum up to [tex]15333[/tex] are [tex]5110, 5111,[/tex] and [tex]5112[/tex]

Hope this helps :)

help anyone?? PLSS ?? ill love u 4eva

Answers

Answer:

4 and 5

Step-by-step explanation:

xy = 20

x + y = 9 ⇒ x = 9 - y

y(9 - y) = 20

9y - y² = 20

y² - 9y + 20 = 0

D = ( - 9)² - 4(1)(20) = 81 - 80 = 1

[tex]y_{1}[/tex] = (9 + 1) ÷ 2 = 5

[tex]y_{2}[/tex] = (9 - 1) ÷ 2 = 4

The numbers are 4 and 5

Which of the following does NOT satisfy the commutative property?
Multiplication with 3x3 matrices
O Multiplication with integers
O Multiplication with complex numbers of the form a + bi
O Multiplication with real numbers

Answers

9514 1404 393

Answer:

  A.  Multiplication with 3×3 matrices

Step-by-step explanation:

Multiplication with real or complex numbers is commutative. Matrix multiplication is not commutative, in general.

3. (05.01)
A consistent, dependent system of equations is a system with ______
(1 point)

Answers

only one line yes yessssssssssdsssssssss

Answer: only one line

Step-by-step explanation:

Write an equation for the following problem.

The cost of a babysitting service on a cruise is $10 for the first hour and $12 for each additional hour. If the total cost of

babysitting baby Aaron was $58, how many hours was Aaron at the sitter?


12x+10=58

10x+12=58


12x-58=10


10x+58=12

Answers

Answer:  Aaron was at the sitter for 5 hours

Step-by-step explanation:

12x + 10 = 58

the 12x is for each hour after the first hour and the 10 is the first hour

-10 from each side

12x = 48

/12

x = 4

4 additional hours plus the original hour

Answer: 12x+10=58

Explanation: $10 is the flat rate, so it only applies to one of the hours. It is not being multiplied by anything. Her hourly rate after that is $12 meanings the amount of money she makes depends on how many hours she works which is x. $58 is the end result so that is what the equation equals.

Write 6 2/7 as an improper fraction.

Answers

Answer: 44/7

Step-by-step explanation:     Hope it helps pls give brainliest

6 2/7= ?/7

multiply 6 by 7

= 6 2/7= 42/7

add 42 and 2= 44

= 44/7

The given mixed number 6 2/7 expressed as an improper fraction is 44/7.

The given mixed numbers s as follows:

6 2/7

To convert the mixed number 6 2/7 to an improper fraction, we can follow these steps:

Multiply the whole number (6) by the denominator (7).

⇒ 6 x 7 = 42

Add the product from Step 1 to the numerator (2).

⇒ 42 + 2 = 44

Write the sum from Step 2 as the new numerator over the denominator (7).

The improper fraction equivalent of 6 2/7 is 44/7.

Therefore, 6 2/7 expressed as an improper fraction is 44/7.

Learn more about the fraction here:

brainly.com/question/10354322

#SPJ6

Will give crown! Help

Answers

Answer: The slope is -5/7

Step-by-step explanation:

Slope is rise/run

The rise is -5, and the run is 7

This is why the slope is -5/7

Answer:

The rise is 6 and the run is 7 6/7

Rachel is buying school supplies. She needs to buy a binder for $4.50, whiteboard markers for $7.00 and some mechanical pencils for $0.29 each. She can spend up to $13.00. Which inequality can be used to find m, the number of mechanical pencils she can buy?

Answers

0.29m + 4.50 + 7 < or equal to 13 ;)

220-450+9
Will mark brainliest ​

Answers

Answer:

220_450×9 =-221

Step-by-step explanation:

I hope l helped you .Please follow me. ❤❤

After 4 new students joined a class, the class had 32 students. Which equation can be used to find n, the number of students in the class before the 4 new students joined? n A 32 Bn -4 = 32 C 4n = 32 Dn+ 4 = 32​

Answers

Answer: D

Step-by-step explanation: if 4 students joined ur adding to the class hope this helps :)

Answer:

The answer is D.

Need help
Question in the screenshot below
NO spam
Please show your work

Answers

Answer:   x = 6

======================================================

Work Shown:

[tex]\log_{4}(x+10)+\log_{4}(x-2)=\log_{4}(64)\\\\\log_{4}\left((x+10)(x-2)\right)=\log_{4}(64)\\\\(x+10)(x-2)=64\\\\x^2-2x+10x-20=64\\\\x^2-2x+10x-20-64=0\\\\[/tex]

[tex]x^2+8x-84=0\\\\(x+14)(x-6)=0\\\\x+14=0 \ \text{ or } \ x-6=0\\\\x=-14 \ \text{ or } \ x=6\\\\[/tex]

Those are the possible solutions, but plugging x = -14 back into the original equation will lead to an error. So we rule x = -14 out

x = 6 works as a solution however

Find the slope of the line that is parallel and perpendicular to the given line.

y = 1/3x + 5

m ll =
⊥ =

Answers

Answer:

|| slope= 1/3

⊥ slope=-3

Step-by-step explanation:

The line is y=1/3x+5

Parallel slopes are the same (think about parallel lines and how they will never intersect- that means that slopes of those lines will never intersect so they have to be the same)

That means that the || slope will be 1/3.

Perpendicular slopes are negative and reciprocal (if you multiply them, they will equal -1)

Which means to solve for the slope perpendicular, use this equation

1/3m=-1

multiply by 3 on both sides

m=-3

So that means the ⊥ slope will be -3.

hope this helps!

Answer:

[tex]\frac{1}{3}[/tex] and - 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{1}{3}[/tex] x + 5 ← is in slope- intercept form

with slope m = [tex]\frac{1}{3}[/tex]

Parallel lines have equal slopes, thus

[tex]m_{parallel}[/tex] = [tex]\frac{1}{3}[/tex]

Give a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{3} }[/tex] = - 3

i need help with this practice problem

Answers

Answer:

Step-by-step explanation:

V of a sphere is (4/3)*pi*r³, and because we have 3 scoops

V = 3* (4/3) * 3.14 * 4³ = 4* 3.14 * 4³ = 803.84 cm³

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