A manufacturer orders lots of steel rods from a supplier (each lot consists of thousands of rods). Assume that the mean length of the rods in each lot is 4 meters and standard deviation is 0.04 meter. The quality manager accepts a lot if the mean length of the randomly selected sample of 64 rods from that lot is at least 4.005 meters, otherwise the lot is returned to the supplier. a) What percentage of the lots received by the manufacturer will be returned to the supplier

Answers

Answer 1

Answer:

84.13% of the lots received by the manufacturer will be returned to the supplier

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 zscore 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 pvalue, 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.

Assume that the mean length of the rods in each lot is 4 meters and standard deviation is 0.04 meter.

This means that [tex]\mu = 4, \sigma = 0.04[/tex]

Sample of 64:

This means that [tex]n = 64, s = \frac{0.04}{\sqrt{64}} = 0.005[/tex]

a) What percentage of the lots received by the manufacturer will be returned to the supplier

The proportion is the pvalue of Z when X = 4.005. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{4.005 - 4}{0.005}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a pvalue of 0.8413

0.8413*100% = 84.13%

84.13% of the lots received by the manufacturer will be returned to the supplier


Related Questions

How many joules of gravitational potential energy are stored in an object that has a mass of 8.5 kilograms and is held 2 meters above the surface of earth?

Answers

Answer:

I believe the answer is 166.6 Joules or (if rounding to the nearest whole number) 167 Joules.

Step-by-step explanation:

Here is the formula to find the gravitational potential energy of an object:

U = m * g * h (potential energy equals mass times gravitational acceleration * the height)

The mass is 8.5 kilograms, the height is 2 meters, and Earth's gravitational acceleration is always, no matter the other values or earthly situations, 9.8 m/s.

Now we solve:

8.5 * 9.8 * 2 = 166.6 which is rounded to 167 Joules.

Jose Luis desea colocar una línea de azulejos alrededor de toda la piscina de su casa. La piscina tiene forma rectangular con un ancho de 10 m y una longitud de 25 m. , ¿cuántos metros lineales de azulejos necesitará comprar?

Answers

Answer:

70

Step-by-step explanation:

2 x (25 + 10) = 2 x 35 = 70

Evaluate the formula for B = 9 in.2 and h = 32 in.

32 in.3

9.6 in.3

96 in.3

288 in.3

Answers

Answer:

is going to give you a decimal as then you divide it by 2 and then multiply that number by 4 hope this helps

Step-by-step explanation:

Answer:

is going to give you a decimal as then you divide it by 2 and then multiply that number by 4 hope this helps

Step-by-step explanation:

Need help plz and thank u

Answers

Answer:

20%

Step-by-step explanation:

12/60 (divided) makes 0.2, converted to a percent is 20%

20% is left to kill my self

A researcher studies differences in career goals between boys and girls in middle school. All of the students in the seventh grade schools in a particular county answer a list of questions. What type of study is this?

A. Experiment
B. Sample Survey
C. Observational Study
D. Random Trial

Answers

Answer:  B) Sample survey

Explanation:

When asking/answering questions like this, a survey is involved. It could be multiple choice or fill in the blank. Multiple choice may be the best way because it's easier to compare data results when you have only a few options. It also gives the computer an easier time too.

We aren't conducting an experiment since the researcher is not directly affecting the people, and instead letting them answer the questions without intervention. Also, note how we don't have two groups of treatment vs control. This is another indication we don't have an experiment.

An observational study is not being done here either. Yes the researcher is observing the survey results, but s/he is not making notes on the individuals before the survey is conducted (ie before the questions are asked). An example of an observational study is having the researcher make a tally of students' hair color. The researcher simply looks at each student, marks the correct tally, and doesn't need to ask the student a question. So you can see that the interactive question/answer portion is not present in an observational study.

The phrasing "random trial" is not a study type. When you hear "random trial" in the news, maybe for a new drug being developed, the news report is implying heavily that an experimental study had been done. This is true with all drug trials. One group is the treatment group that gets the actual drug, while the control group gets a fake drug. The control group thinks they get the actual drug, which is important because if they knew it was fake, then it would invalidate the study. I recommend researching the placebo affect for more information. The two group's results are then computed to see if the drug did in fact cause a change in the subjects or not. You would see this if there's a significant difference between the treatment and control group. Anyway, the "random trial" is not a study type but rather an aspect of an experimental study. It's possible your teacher put this in here to throw off students.

The number of swings in use on average is.

Answers

Answer:

?

Step-by-step explanation:

Use the distributive property to simplify the following expression: 3 (2 + 5z)​

Answers

The answer is 6+15z

The length of a cell phone is 1.41.4 inches and the width is 4.44.4 inches. The company making the cell phone wants to make a new version whose length will be 1.751.75 inches. Assuming the side lengths in the new phone are proportional to the old phone, what will be the width of the new phone?

Answers

Answer:

Step-by-step explanation:

Answer:

5.573.75

Step-by-step explanation:

because math

What is the value of c so that −15 and 15 are both solutions of x^2−c=157?

Answers

Answer: -c= 157+X^2

Step-by-step explanation:

Select the correct comparison.
Set A
Set B
.
....
24
8 10
4 6 8 12
A. The typical value and the spread are both greater in set B.
B. The typical value and the spread are both greater in set A.
C. The typical value is greater in set A. The spread is greater in set B.
D. The typical value is greater in set B. The spread is greater in set A.

Answers

Answer:i would say C ADHAKFFA

Step-by-step explanation:

Rackham Graduate School has 8,000 students (5,000 PhD students and 3,000 masters stu- dents). The Rackham Student Government Executive Board has 4 student members: a President, a VP of Operations, a VP of Finance, and a VP of Administration. Reminder: no need to simplify your answers in this homework (unless problem explicitly says to).
a) How many ways are there to choose the Exec Board from all Rackham students?
b) How many ways are there to choose the Exec Board so that there is at least one masters student and one PhD student? (for any of the 4 positions)
c) How many ways are there to choose the Exec Board if the VP positions have to be PhD students (the president can be either a PhD or Masters student)?
d) How many ways are there to choose the Exec Board so that there is at least one masters student VP?

Answers

Answer:

a) 8,000!/(8000 - 4)! ways

b) 15,000,000 + 7998!/(7998 - 2)! ways

c) 5,000 + 7,999!/(7,999- 3)! ways

d) 3,000 + 7,999!/(7,999- 3)! ways

Step-by-step explanation:

The number of students at Rackham Graduate School = 8,000 students

The number of PhD students = 5,000

The number of masters students = 3,000

The number of student members of the Rackham Student Government Executive Board = 4 students

a) The number of ways there are to choose the Exec Board from all Rackham students = The number of ways to choose 4 students from 8,000 = 8,000!/(8000 - 4)!

b) The number of ways of having one Master student in the board = 3,000 ways

The number of ways of having one PhD student in the board after selecting a masters student = 5,000 ways

The number of ways of selecting the remaining 2 members =

7998!/(7998 - 2)!

The total number of ways of selecting at least one masters and one PhD in the board is therefore equal to 5,000 × 3,000 + 7998!/(7998 - 2)! ways

c) The number of ways of choosing the VP position as PhD = 5,000 ways

The number of ways of choosing the other three members = 7,999!/(8000 - 3)!

Therefore, the total number of ways = 5,000 + 7,999!/(7,999- 3)! ways

d) The number of ways of choosing a masters student as the VP position = 3,000 ways

The number of ways of choosing the other three members = 7,999!/(8000 - 3)!

Therefore, the total number of ways = 3,000 + 7,999!/(7,999- 3)! ways

Solve for x Enter the solutions from least to greatest . (x - 4)(- 5x + 1) = 0 lesser x = greater x =

Answers

Answer: lesser x = 1/5 greater x = 4

Step-by-step explanation:

What quadrant does 21pi/4 lie in?

Answers

Answer:

The angle is in the third quadrant.

6) Solve:
5x + 12 + 3x = 8x - 5

Answers

Answer: −17

Step-by-step explanation: ez

Hope this helps !!!!!

34+35? :)))) answer immediately

Answers

Answer:

69

Step-by-step explanation:

30+30=60

4+5=9

60+9=69!

What is the slope of the line that goes through (-3, 2) and (3, 2)?​

Answers

Answer:

m = 0

Step-by-step explanation:

Hope this helps:)

How is math used in making murals?(subject:Collage and Career readiness)

Answers

she 56/92 6-5=1 and 567-1=566

Tanner collected 360 cans and bottles while fundraising for his basketball team This was 40% less than what Reggie collected How many cans and bottles did Reggie collect?​

Answers

Answer:

Reggie collected 504 cans and bottles.

Step-by-step explanation:

40%=.40

360*.40=144

360+144=504

Jeff and George each have a box of popcorn. How much more popcorn does the bigger box hold than the smaller box?

Answers

Answer:

there in not enough information in your question to get an answer

Answer:

Part 1: Jeff Part 2: 130

Step-by-step explanation:

Write 8 1/5 as a fraction

Answers

Answer:

8.2

Step-by-step explanation:

let me know if its wrong

Select the correct answer. Sarah owns a flower shop and can model the profits from selling springtime bouquets using this equation, where b is the number of springtime bouquets. P = -5b^2 + 450b - 1,000
Which statement is true if Sarah needs to make a profit of at least $9,000?
A. Sarah must sell more than 90 bouquets.
B. Sarah must sell between 40 and 50 springtime bouquets.
C. Sarah must sell between 0 and 40 springtime bouquets.
D. Sarah must sell more than 50 springtime bouquets.​

Answers

Answer:

B

Step-by-step explanation:

If you plug in the answers for guess and repeat this one works.

The correct statement is Sarah must sell between 40 and 50 springtime bouquets true if Sarah needs to make a profit of at least $9,000.

Given that,

Sarah owns a flower shop and can model the profits from selling springtime bouquets using this equation,

Where b is the number of springtime bouquets, [tex]P = -5b^2 + 450b - 1,000[/tex].

We have to determine,

Which statement is true if Sarah needs to make a profit of at least $9,000.

According to the question,

Sarah owns a flower shop and can model the profits from selling springtime bouquets using this equation,

[tex]P = -5b^2 + 450b - 1,000[/tex]

Divide the equation by -5,

[tex]P = -5b^2 + 450b - 1,000\\\\P = -b^2 + 90b - 200[/tex]

Factorize the equation for the value of profit,

[tex]b^2 - 90b +200 = 0\\\\b^2 -50b -40b +200= 0\\\\b ( b-50) - 40(b-50) = 0 \\\\(b-50) (b-40) = 0 \\\\b- 50 = 0, \ b = 50\\\\b - 40 = 0, \ b = 40[/tex]

Hence, Sarah must sell between 40 and 50 springtime bouquets.

To know more about Quadratic equations click the link given below.

https://brainly.com/question/22364785

Gina tosses a number cube 66 times. About how many times would you expect that Gina would toss a 6?​

Answers

Answer:11

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

its 11 because 66 divided by 6 = 11

An electronics store is having a 15% off sale. Suppose the sale price(p) of a laptop is $495. Which statement are true for this stuation
A. P+ 0.15p represents the sales price
B. P- 0.15p represent the sales price
C. 0.85p represents the sales price
D. The sale price is 420.75
E. The sale price is 569.25

Answers

Answer:

The answer to the Question is D

Answer:

B, C, D

Step-by-step explanation:

If the sales price is 15% off, then the the price is .85(100-15%) of the price so c is true

this also makes b true. (100-15%) is p-.15

495 x .85 (100-15%)=420.75 so d is true

Find the measure of 2.
50 2.
1130
< 2 =
[?]

Answers

= 180° - 50°
= 130°

the answer is 130°

CL 6-153
In 2012 the average cost for a new midsized car was about
$31,000. New car prices tend to go up about 2% every year.
a. What is the multiplier for this situation?
b. If this trend continues, what will the cost be in 4 years?
c. Write an equation to calculate the cost in n years. What does
each of the factors in your equation represent?

Answers

Answer:

A) The multiplier for this situation is 0.02.

B) The cost in 4 years will be $ 33,555.39.

C) 31,000 x 1.02 ^ N = X

Step-by-step explanation:

Since in 2012 the average cost for a new midsized car was about $ 31,000, and new car prices tend to go up about 2% every year, to determine what is the multiplier for this situation, what will the cost be in 4 years if this trend continues and to write an equation to calculate the cost in n years the following calculations must be performed:

A)

31,000 x 2/100 = X

31,000 x 0.02 = X

Thus, the multiplier for this situation is 0.02.

B)

31,000 x 1.02 ^ 4 = X

33,555.39 = X

Thus, the cost in 4 years will be $ 33,555.39.

C)

31,000 x 1.02 ^ N = X

Here, N represents the number of years over which the price increase will be calculated, and X represents the price after that number of years.

Shawn buys 15 shirts for a total of $60. Express this as an equation using 'X' as the cost of each shirt.​

Answers

Answer:

15x = 60

Step-by-step explanation:

Hi,

We know he bought 15 shirts for an x amount of dollars, so 15 times however much they cost is 15x and the total is 60.

hope this helps :)

1) f(x) = 3*
f(x)
x
-1
0
1
2 3

Answers

1)f(×)=3*=f(×)=×-1 0 1=0.23

What is the value of x?

Enter your answer in the box.

X=l_l

Answers

9514 1404 393

Answer:

  x = 62

Step-by-step explanation:

The angle marked x° is shown as the complement of the angle marked 28°. This means ...

  x = 90 -28 = 62

with one of these is a function
a
b
c
d​

Answers

Answer:

It's B

Step-by-step explanation:

Answer:

B is a functional answer

Graph the inequality.
x > 4

Answers

Answer:

Step-by-step explanation:

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