A manufacturing process is designed to produce bolts with a 0.75-inch diameter. Once each day, a random sample of 36 bolts is selected and the bolt diameters recorded. If the resulting sample mean is less than 0.730 inches or greater than 0.770 inches, the process is shut down for adjustment. The standard deviation for diameter is 0.04 inches. What is the probability that the manufacturing line will be shut down unnecessarily

Answers

Answer 1

Using the normal distribution and the central limit theorem, it is found that there is a 0.0028 = 0.28% probability that the manufacturing line will be shut down unnecessarily.

In a normal distribution 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]

It 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, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n have standard deviation given by [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

In this problem:

Mean of 0.75 inches, thus [tex]\mu = 0.75[/tex].Standard deviation of 0.04 inches, thus [tex]\sigma = 0.04[/tex]Sample of 36, thus [tex]n = 36, s = \frac{0.04}{\sqrt{36}} = 0.0067[/tex].

The probability of being shutdown is the probability of a sample mean less than 0.73 inches or more than 0.77 inches. They are the same distance to the mean(0.02), thus, considering the Central Limit Theorem:

[tex]z = \frac{0.02}{s}[/tex]

[tex]z = \frac{0.02}{0.0067}[/tex]

[tex]z = 2.99[/tex]

The probability is P(|z| > 2.99), which is 2 multiplied by the p-value of z = -2.99.

z = -2.99 has a p-value of 0.0014.

2(0.0014) = 0.0028

0.0028 = 0.28% probability that the manufacturing line will be shut down unnecessarily.

A similar problem is given at https://brainly.com/question/25212662

Related Questions

A car is traveling at a steady speed. It travels 1 3/4 miles in 2 1/3 minutes. How far will it travel in 25 minutes? In 1 hour?

Answers

Answer: They would travel 17.25 miles in 23 minutes and 45 miles in 1 hour.

Step-by-step explanation:

If you divide 1 3/4 by 2 1/3 you get. 0.75 which is how far the car will travel each minute and then you can just multiply that number by however many minutes there are.

Find g(x) for each x value in the table

Answers

Answer:

-2 = -2/7

-1= -1/7

0=0

1= 1/7

2= 2/7

Step-by-step explanation:

it gives you a function of 1/7 so you multiply it by x and u get the g(x) also know as Y

CLASS 6 MATHS!!!! HELP ME PLEASE!!!!!!!

Answers

Step-by-step explanation:

[tex] \\ 20. \: \: ( \frac{ - 3}{4} )(4\frac{1}{6} )[/tex]

[tex] \\ = \frac{ - 3}{4} \times \frac{25}{6} [/tex]

[tex] \\ = \frac{ - 25}{8} [/tex]

[tex] \\ = - 3.125[/tex]

[tex] \\ 21. \: \: ( - 3\frac{7}{8} )( - 5\frac{3}{4} )[/tex]

[tex] \\ = \frac{ - 31}{8} \times \frac{ - 23}{4} [/tex]

[tex] \\ = \frac{713}{32} [/tex]

[tex] \\ = 22.28125[/tex]

Estimate the difference by rounding each number to the nearest whole

367.2-294.8
A. 72
B.72.4
C.73
D.80

Answers

Answer:

A. 72

Step-by-step explanation:

367.2 -> 367

294.8 -> 295

367

- 295

____

072

if you weren't estimating you would get B because you wouldn't round the numbers.

since the question says to round and then estimate, the answer should be A.

Karen is joining a book club. To join, she must buy two books, and then she will get one free book. The following are the prices for the 8 books being offered: A. $29.50 E. $16.25 B. $25.00 F. $19.98 C. $18.00 G. $49.00 D. $39.50 H. $17.98 Karen wants to select her books with the maximum dollar value and yet pay as little as possible. What three books should she select? A) A, C, D
B) A, B, G
C) C, E, H
D) E, G, H

Answers

Answer:

the answer are is c,e,h because they have low prices

Zaby does 15 Joules of work to push the pencil over 1 meter. How much force did he use?

Answers

When converted to a household measurement, 9 kilograms is approximately equal to a

Find the quotient or 4/5 and 6/7 give ur answer as a fraction in simplest form

Answers

Answer:

14/15

Step-by-step explanation:

Let me know if i got it right if not I'm sorry :(

The required quotient would be 14/ 15 which is a fraction.

What is the Quotient?

A quotient is defined as the outcome of dividing an integer by any divisor that can be said to be a quotient. The dividend contains the divisor a specific number of times.

We have been given that two numbers are 4/5 and 6/7

To determine the quotient or 4/5 and 6/7

⇒ 4/5 ÷ 6/7

⇒ 4/5 / 6/7

Reciprocal the term of denominator,

⇒ 4/5 × 7/6

Apply the multiplication operation,

⇒ 28 / 30

Reduce the above fraction to the simplest form

⇒ 14/ 15

Therefore, the required quotient would be 14/ 15 which is a fraction.

Learn more about the quotient here:

brainly.com/question/27796160

#SPJ2

PLEASE, I need help ASAP !

Answers

Answer:

I'm not 100% sure but I think it's C.

it might also be B. it's one of those 2 for sure but I'm like %80 sure it’s C.

Step-by-step explanation:

please let me know if im right or wrong....

Answer:

you said you're giving 15 points but its 8

Dilate the figure by the scale factor. Then enter
the new coordinates.
K = 2

Answers

Answer:

A = (-6, 4)

B = (2,2)

C = (-2, 2)

Step-by-step explanation:

If a coordinate (x, y) is dilated by a factor of k, the resulting coordinate will be expressed as (kx, ky). Note that each coordinate is multiplied by the scale factor Given the coordinates (-3,2),(1,1)(-1,-1), if they are dilated by a factor of 2, the resulting coordinate will be;

A = (2(-3), 2(2)) = (-6, 4)

B = (2(1),2(1)) =(2,2)

Answers

Answer:

Step-by-step explanation:

Multiply the term (4) by the common ratio (4)

4 * 4 = 16

What is the slope of 3x+4y=−2?

Answers

Answer:

subtract the 3x from one side and put in the other

4y = -3x -2

then divide both sides by 4

y= -3/4x -1/2

A city has a population of 280,000 people. Suppose that each year the population grows by 4.75% . What will the population be after 7 years ? Use the calculator provided and round your answer to the nearest whole number.

Answers

8.75% = 0.0875 P(t) = Initial Population * (1 + rate)t P(t) = 280,000(1 + 0.0875)t P(t) = 280,000(1.0875)t P(9) = 280,000(1.0875)9 P(9) = 595,692

is 0 a natural number or a whole number

Answers

Answer:

O is a whole number.

Step-by-step explanation:

Answer:

0 is not a natural number, it is a whole number.

Step-by-step explanation:

Negative numbers, fractions, and decimals are neither natural numbers nor whole numbers. N is closed, associative, and commutative under both addition and multiplication (but not under subtraction and division).

Who can help me with this entire page?

Answers

Answer:

I'm not entirely sure what the question is but every thing under 12.5 is closer to 12, everything 12.5 and upwards like 12.87 would be closer to 13

solve pls brainliest

Answers

Answer:

4.5341 < 6.9 < 6.906 < 6.96

Step-by-step explanation:

4.5341 is closer to 0 than 6.96 is.

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