Parts being manufactured at a plant are supposed to weigh 65 grams. Suppose the distribution of weights has a Normal distribution with mean 75 grams and a standard deviation of 22 grams. Quality control inspectors randomly select 144 parts, weigh each, and then compute the sample average weight for the 144 parts. Find The probability that the mean weight of these 144 parts is more than 80 grams or less than 70 grams is (Round to two decimals throughout and write as a % to 2 decimal places)

Answers

Answer 1

Answer:

0.64%.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 75 grams and a standard deviation of 22 grams.

This means that [tex]\mu = 75, \sigma = 22[/tex]

Sample of 144:

This means that [tex]n = 144, s = \frac{22}{\sqrt{144}} = 1.8333[/tex]

More than 80 or less than 70:

Both are the same distance from the mean, so we find one probability and multiply by 2.

The probability that it is less than 70 is the pvalue of Z when X = 70. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{70 - 75}{1.8333}[/tex]

[tex]Z = -2.73[/tex]

[tex]Z = -2.73[/tex] has a pvalue of 0.0032

2*0.0032 = 0.0064.

0.0064*100% = 0.64%

The probability is 0.64%.


Related Questions

6. Write the formula of circumference
of a circle when its diameterld)
is given.​

Answers

Step-by-step explanation:

nl the way home now so I'm gonna get

Circumference = pi • diameter
C= (pi symbol)d

(I don’t have a pi symbol on here)

4. Joe likes sports. He has 4 soccer medals, 1 tennis medal, 3 swimming medals and 5
football medals.
What is the ratio of Joe’s soccer medals to swimming medals?
A. 4 to 1
B. 1 to 3
C. 3 to 5
D. 4 to 3
E. 1 to 12

Answers

Answer:

4:3

Step-by-step explanation:

He has 4 Soccer Medals, 3 Swimming Medals

So it would be 4:3

In a class of 30 students, 12 have a brother and 25 have a sister. There are 2 students who do not have any siblings. What is the probability that a student who has a brother also has a sister?​

Answers

12 I think , actually I am not sure about this , if it is wrong count on me

what does x and y =??????

Answers

Answer:

x=30. y=60

Step-by-step explanation:

DG is a straight segment so it sums to 180 degrees. ECG is a right angle so 90 degrees. The rest is described as 2x and x. So 3x=90 degrees. x=30. Eh is also a straight segment. since we know x, we know that ECD is 60 degrees. So y+y=120 degrees. 2y=120. y=60.

Line ABC is a straight line
Which descnbes the relationship between 21 and 22?
21 and 22 are complementary angles.
21 and 22 are supplementary angles.
21 and 22 are vertical angles
21 and 22 are acute angles

Answers

Answer:

angle 1 and angle 2 are supplementary angle

Answer: the answer is b

Step-by-step explanation:trust

Please answer the following question

Answers

How many cars are there? If you say how many in the comments I’ll answer

NEED URGENT HELP correct answer person will get brianly and extra pts

Answers

Answer:

7

Step-by-step explanation:

The blue whale, the fastest marine mammal, can travel 60 miles in 2 hours. The fastest fish, the sailfish, can travel 136 miles in 2 hours. How much faster is the sailfish than the blue whale?
A. 76 mph faster
B. 58 mph faster
C. 38 mph faster
D. 26 mph faster

Answers

Answer:

c 38

Step-by-step explanation:

i got it right on the quiz

Answer:

C

Step-by-step explanation:

how do I get the answer to this​

Answers

you should divide or simplify the problem.

Which features are present in this polar graph?

Answers

The features that is present in this polar graph is that A. Symmetry about the polar axis θ = 0.

What is true of the polar graph?

The polar graph can be said to have a symmetry about the polar axis which means that theta or θ is equal to 0.

This is because the graph is symmetric about the x-axis. This means that all the lines of symmetry can be seen intersecting the graph at x = 0. This proves that there is indeed symmetry in the polar graph.

In conclusion, option A, θ = 0 is correct.

Find out more on polar graphs at https://brainly.com/question/22692278

#SPJ1

y = 5x + 4 and y =- 5x -6

Answers

Answer:

there you o plz can u mark me brainlest

Step-by-step explanation:

5x+4         -5x-6

m=5           m=-5

what is 2x2+2i know the answer but you answer it

A. 1

B. 3

C.2

D.6​

Answers

The answer is D, 6 :)
D thats becuase if you do 2x2 it equals 4 and if you add 4 + 2= that'll be 6.

Please Classify ∠1 and ∠2 using all names that apply

Answers

Answer:

Supplimentery angles

If the sum of the measures of two angles is 180 degrees, then the angles are supplementary angles.

Answer:

∠1 & ∠2 are supplementary angles & they form a linear pair. (option D)

Work out the answer when,
'the largest prime number that is a factor of 35'
is multiplied by
'the smallest prime number that is a factor of 12'.
[2]

Answers

Answer:14

Step-by-step explanation:

The largest Prime factor of 35 is 7 (factors of 35 are 1,5,7,35)

the smallest prime factor of 12 is 2 (factors of 12 are 1,2,3,4,6,12)- and 1 is not Prime

7*2=14

2d+7/6-d-5/3=0 Tell me the answer ​

Answers

Answer:

D=1/2

Step-by-step explanation:

Multiply the numbers

Subtract the numbers

Combine like terms

put 1/2 to the two parts of the equation

last but not least, simplify

Estimate the given rotation within 10 degrees:

Answers

Answer:

70∘

Step-by-step explanation:

What does x equal? A. 4 B. 2 C. -2

Answers

Answer:

i.d.k

Step-by-step explanation:

Which is bigger a population or a sample?
a - Population
b - Sample
c - They are both the same

Answers

Sorry I need points

Find the perimeter of the semicircular region. Round your answer to the nearest hundredth.
6 in.

Answers

9514 1404 393

Answer:

  30.85 in

Step-by-step explanation:

The circumference of a circle with a 6" radius is ...

  C = 2πr

  C = 2π(6 in)

Then the curved portion of a semicircle with that radius will have the length ...

  1/2C = 1/2(2π)(6 in) = 6π in . . . . curved length

The straight portion of the boundary of this figure is simply twice the radius, so is ...

  2×6 in = 12 in . . . . straight length

__

The perimeter is the sum of the curved and straight lengths:

  P = (6π +12) in ≈ 30.8496 in ≈ 30.85 in . . . . figure perimeter

what is the slope for this graph ?

Answers

Answer:

um 6/1?

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

The slope of a line is the change in the line. It is often referred to as the ([tex]\frac{rise}{run}[/tex]), the slope of the line can be found using the following formula,

[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

The graph of the given line gives one the points (7, 2), (9, 6). Substitute these points into the given formula and solve for the slope,

[tex]\frac{6 - 2}{9 - 7}[/tex]

Simplify,

[tex]=\frac{4}{2}[/tex]

[tex]=2[/tex]

) A different rectangle has area 12a² and perimeter 14a
What are the dimensions of this rectangle?
Dimensions:
. by​

Answers

Answer:

l = 4a and b = 3a

Step-by-step explanation:

Given that,

The area of the rectangle, A = 12a²

Perimeter, P = 14a

The area and perimeter of a rectangle are given by :

A = lb

12a² = lb ....(1)

P = 2(l+b)

14a = 2(l+b) ....(2)

We need to solve equations (1) and (2). After solving we find that.

l = 4a and b = 3a

Hence, the dimensions of this rectangle are 4a and 3a.

If the outside diameter of a pipe is 1.25 ft and the inside diameter is 0.975 ft how thick is the pipe

Answers

Answer:

0.275

Step-by-step explanation:

1.25-0.975=0.275

See below
Answer: .1375

See explanation:


1.25-0.975=.275

Now since this gives you the difference between the outside diameter and the inside diameter it actual gives you 2 times the wall thickness. So we need to divide that by 2.

.275/2=.1375

So the wall thickness of the pipe is .1375

7) Rob and Amy are selling cheesecakes for a school fundraiser. Customers can buy New York
style cheesecakes and chocolate marble cheesecakes. Rob sold 11 New York style cheesecakes
and 7 chocolate marble cheesecakes for a total of $266. Amy sold 4 New York style cheesecakes
and 14 chocolate marble cheesecakes for a total of $280. What is the cost each of one New York
style cheesecake and one chocolate marble cheesecake?

Answers

9514 1404 393

Answer:

New York style: $14Chocolate Marble: $16

Step-by-step explanation:

We can let n and c represent the costs of the New York style and the chocolate marble cheesecakes, respectively. Then the two sales are ...

  11n +7c = 266 . . . . . . . Rob's sale

  4n +14c = 280 . . . . . . Amy's sale

The ratio of coefficients of c is a "nice" number (2), so we can eliminate the c variable easily to solve this. Dividing the second equation by 2 and subtracting it from the first gives ...

  (11n +7c) -(1/2)(4n +14c) = (266) -(1/2)(280)

  9n = 126 . . . . . . simplify

  n = 14 . . . . . . . . divide by 9

Filling this into the first equation, we have ...

  11(14) +7c = 266

  7c = 112 . . . . . . . . subtract 154

  c = 16 . . . . . . . divide by 7

One New York style cheesecake costs $14; one chocolate marble cheesecake costs $16.

What is the value of x in the figure shown below?

Answers

The value of X is 35 because the angle 35 measures the same as the angle X, hence their values are the same

a square has the side length (x+5) units whats is its area

Answers

Answer:

25 square units

Step-by-step explanation:

Hope this helps :)

the nutrition information on the cereal box says that a 1/2-cup serving provides 210 calories and 6 grams of dietary fiber. at that rate, find how many calories and grams of fiber are in a 1/3-cup serving

Answers

Answer:

140 Calories and 4 grams of dietary fiber per 1/3-cup serving.  

Step-by-step explanation:

hi you can find this by first doubling the amounts for a 1/2 cup serving

so then it is equal to a full cup serving.

and then divide those by three,

that way it will be equal to 1/3 cup serving.

so

210*2= 420 (lol)

6*2= 12

now divide these numbers by 3

420/ 3 = 140

12/3= 4

so your answers are

140 Calories and 4 grams of dietary fiber per 1/3-cup serving.

I hope this helps! Good luck!

Joe has $32.40. He wants to buy several comic books that each cost $2.70. How many comic books can he buy?

Answers

Answer:

12

Step-by-step explanation:

$32.40/$2.70 = 12 comic books :)

Answer:

Joe has 12 comic books

Step-by-step explanation:

32.40 ÷ 2.70 = 12

check our answer : 2.70 × 12 = 32.40

Therefore, the answer is Joe has 12 comic books

LCM OF (2^3×3×5) and (3×5) is



(a)8
(b)120
(c)40
(d)180​

Answers

Answer:

120

Step-by-step explanation:

2³* 3 * 5

3*5

LCM = 2³ * 3 * 5 = 8 * 3 * 5 = 120

someone please answer this!!

Answers

Answer:

130

Step-by-step explanation:

41 plus 9 equal 50 then u minus 50 from 180 and get

130

Answer:

b = 40km is the answer.

Step-by-step explanation:

a = 9km

b = ?

c = 41km

By using the Pythagoras theorem,

a² + b² = c²

9² + b² = 41²

81 + b² = 1681

b² = 1681 - 81

b² = 1600

b = 40km

∴ b = 40km is the length of the missing leg.

10.) Find values of x and y for which ABCD must
be a parallelogram.
A x=2 y=4
B x=2 y=6
C x=2 y=16
D x=6 y=2

Answers

Answer:

B x=2 y=6

Step-by-step explanation:

For ABCD to be parallelogram, following conditions should be satisfied:

2x - 0 = x + 2 & 4y - 8 = y + 10

2x - 0 = x + 2

2x - x = 2

x = 2

4y - 8 = y + 10

4y - y = 10 + 8

3y = 18

y = 18/3

y = 6

Other Questions
please help ill give brainliest PLEASEEE HELP ASAP! BRAINLIST GETS 80 POINTS!!!!!!!!!!04.02 Environmental Resources Lab ReportInstructions: For this lab, use the lab report to record your information. You will submit your completed lab report. Note: If you cannot complete this lab as directed, please contact your instructor for assistance.Name and Title: Include your name, instructor's name, and date. Introduction To improve your soil, you should first know what youre starting with. In this lab, you will sample local soil to determine its composition and pH range. Materials Distilled water Metric ruler Small zipper storage bag Soil from the yard, garden, or other local source Jar with tightly fitting lid (tall and skinny would be best) Small digging tool pH strips (available at hardware and pool supply stores) or vinegar and baking sodaPre-lab Questions1. Describe soil particles (sand, silt, and clay) in term of size and texture.2. If soil is too acidic, what substance is usually added? If soil is too alkaline, what substance is usually added?3. Why are soil composition and pH important to know?HypothesisPredict what type of soil you think is in your local area (mostly sand, silt, clay, or mixed) and if it more acidic, more alkaline, or neutral.ProcedureObtaining soil samples for your jar and resealable bag1. Take your jar, resealable bag, and digging tool into your garden or yard. Use the digging tool to dig a hole 36 inches deep. Take your soil sample from the soil at this depth.2. Place approximately one cup of soil into the resealable bag, squeeze the air out of the bag, and zip it shut (you will use this soil later in the lab).3. Dig up additional soil and fill the jar to approximately 1/4 full of soil. Take everything back inside to your work area.Note: To avoid making a mess, it is best to work on a covered surface (for example, a kitchen counter covered with old newspaper or plastic wrap).4. Fill the remaining space in the jar with water, and screw the cap on tightly (see Figure 1, below).5. Shake the jar so that the dirt is totally dispersed through the water (see Figure 2, below). Set down the jar and allow the shaken contents to settle completely (see Figure 3, below). Leave it undisturbed overnight while you test the texture and pH of the soil in your resealable bag.Note: Do not pick up the jar. Doing so will begin to mix the contents again.Figure 1 Figure 2 Figure 3Fill jar 3/4 full of water and 1/4 full of soil. With the lid on tightly, shake the jar well until the soil and water have mixed thoroughly. Let the jar sit. Materials will begin to settle out and form layers.Testing texture and pH of the soil in your resealable bag1. While you wait for the soil and water sample to settle in the jar, you can test the texture of the sample in the resealable bag. First, remove a small amount and moisten it slightly to test the texture. Record your observations in the Data and Observations section.a. Rough and gritty soil that barely sticks together is sand.b. Loams (mixtures of clay, silt, and sand) feel medium-textured.c. Smooth and sticky fine textures indicate clay.2. Next, test the pH using one of the following methods:a. If you have pH strips: To test with pH strips, place the soil sample in a small bowl or container and add a small amount of distilled water. Add just enough water to make the soil slightly liquid, like a milkshake consistency. Dip the pH strip in and compare it to the color identification provided with the test strips. Record your data in the Data and Observations section. b. If you do not have pH strips: Use vinegar and baking soda instead. To do this, split the sample into two containers. Add a half cup of vinegar to the first sample of soil, mix gently, and watch to see if it bubbles or fizzes. If it does, it is alkaline. In the second container, add a half cup of distilled water to the soil and mix gently. Then add a half cup of baking soda. If there is a reaction of bubbles or fizzing, the soil is acidic. If neither sample has a reaction, the soil is neutral. Record your data in the Data and Observations section.Testing soil sample in your jar1. For the sample in the jar, wait until after the contents have settled and you can see several different-colored layers. In addition, you may see some material floating at the top of the water. You may also see that the water is still clouded with some particles. 2. Measure the total thickness of the soil in the jar after it settles. Record this measurement (in centimeters) in the data table.3. Observe the settled dirt carefully. There should be distinct layers of soil. The bottom will be your sand layer (largest particles fall out first), then clay or silt, depending on the kind of soil you have. 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