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

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.

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!

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

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 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]

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.

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

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

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

Please answer the following question

Answers

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

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)

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

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.

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

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 :)

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.

) 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.

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:

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

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

Answers

Answer:

7

Step-by-step explanation:

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

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)

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

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

Answers

Sorry I need points

how do I get the answer to this​

Answers

you should divide or simplify the problem.

Estimate the given rotation within 10 degrees:

Answers

Answer:

70∘

Step-by-step explanation:

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

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

Answers

Answer:

i.d.k

Step-by-step explanation:

Other Questions
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