The lengths of 3-inch nails manufactured on a machine are normally distributed with a mean of 3.0 inches and a standard deviation of .009 inch. The nails that are either shorter than 2.98 inches or longer are than 3.02 inches are unusable. What percentage of all the nails produced by this machine are unusable?

Answers

Answer 1

Using the normal distribution, it is found that 2.64% of all the nails produced by this machine are unusable.

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.

In this problem:

The mean is of 3 inches, hence [tex]\mu = 3[/tex].The standard deviation is of 0.009 inches, hence [tex]\sigma = 0.009[/tex].

Nails that are more than 0.02 inches from the mean are unusable, hence:

[tex]Z = \frac{0.02}{\sigma}[/tex]

[tex]Z = \frac{0.02}{0.009}[/tex]

[tex]Z = 2.22[/tex]

The proportion is P(|Z| > 2.22), which is 2 multiplied by the p-value of Z = -2.22.

Z = -2.22 has a p-value of 0.0132.

2 x 0.0132 = 0.0264

0.0264 x 100% = 2.64%

2.64% of all the nails produced by this machine are unusable.

You can learn more about the normal distribution at https://brainly.com/question/24663213


Related Questions

A business owner is comparing the cost of buying natural gas from two different companies.
• Company A charges a $6 fee plus $1.25 per therm (unit of heat).
• Company B charges a $9 fee plus $0.75 per therm (unit of heat).
For what number of therms will the cost be the same at both companies?
13.5 therms
9 therms
6 therms
12.75 therms

Answers

Answer: C. 6 therms

Step-by-step explanation:

6 + 1.25(6) = $13.50

9 + 0.75(6) = $13.50

Correct me if I am incorrect.

How here we get 2 x 22 x 10

And how we multiply the formula of pi with any number

Answers

Answer:

The formula of pi is approximately 3.14 2×3.14

which of the points does not fall on the same line as the other three points? (-4,4) (0,2) (2,1) (4,-1)​

Answers

Answer:

Given (-4,4),(0,2),(2,1),(4,-1)

Only any two points are on the same line.

Step-by-step explanation:

You could do a lot of calculations, write the equations for the points in the line. These would be very good. But, you could also just look at the points on a graph. See image.

Repost if there are different points in the original problem.

I rlly don’t understand due today please help!

Answers

Answer:

a) 2x+4

b)x=8

Step-by-step explanation:

a) x+x+4 =2x +4

b) 2x+4= 20

2x = 16

x=8

Jay bought 8 packets of Chips

c) Jay: 8 x 60

=£4,80

Lauren : 12 × 60

= £7,2

what is the term to term rule for 2 6 18 54 162

Answers

The rule is 3x. The numbers are multiplied by 3 each time.

Answer:

It's always × by 3

Step-by-step explanation:

2×3=6

6×3=18

18×3=54

54×3=162

PLEASE HELP I NEED ANSWERS!!

Answers

Step-by-step explanation:

2. Commutative Property of Multiplication

3. Associative Property of Multiplication

4/5/6 Distrubtitive Property.

Write the equation of the line that has slope 1 half and passes through (4, -1).

Answers

Answer:

-1 = 1/2*4 + -3 / -1 = 1/2*4 - 3 for slope intercept equations

y + 1 = 1/2(x - 4) for point slope equations

Step-by-step explanation:

Slope intercept formula is y = mx  + b where y is the y point, x is the x point on the graph, m is the slope and b is y intercept. For this we know the slope, the x and the y axis. Now all we need to find is the y intercept, for this we would have have to multiply the x axis by the slope and then find the number to complete the equation in this case its 1/2 (slope) and 4 (x axis),

-1 = 2 + b

for this we'd subtract -2 to both sides

-1 -2 = +2 - 2 + b

Which then we'd get,

-3 = b

So our Y intercept is -3

To complete the equation we'd finish it with putting everything together,

-1 = 1/2*4 + -3 or -1 =1/2*4 -3

If it were a point slope equation (y - y₁ = m(x - x₁)) we have the y₁, x₁ and the slope value 1/2, so we have all we need to fill in the point slope equation and here it is,

y + 1 = 1/2(x - 4)

Hope this helps!

45 + 30 = 100 - w


Answer:



Explanation:

Answers

Answer:

w = 25

Step-by-step explanation:

45+30 = 100 - w75 = 100 - ww = 100 - 75w = 25
In order to work out “w”, you could begin by working backwards, starting with 100, then doing the inverse operation (subtracting 30 then subtracting 45).

100 - 30 = 70 - 45 = 25.

100 - 25 = 45 + 30

w = 25

Twelve is sixteen less than four times a number. Write it as a mathematical statement.

Answers

Answer:

12=4x-16

x would represent the unknown number.

Tell which line contains each point for triangle ABC.
the circumcenter
the orthocenter
the centroid
the incenter

Answers

5. The line that contains the circumcenter in ΔABC is: line k.

6. The line that contains the orthocenter in ΔABC is: line m.

7. The line that contains the centroid in ΔABC is: line l.

8. The line that contains the centroid in ΔABC is: line n.

What is the Circumcenter of Triangle?

Circumcenter is the point where all three perpendicular bisectors of the three sides of a triangle meet and they are of equal distance from the three vertices of the triangle.

The line that contains the circumcenter in ΔABC is: line k.

What is the Orthocenter of a Triangle?

Orthocenter is the point in a triangle where the three altitudes that are perpendicular to the opposite sides and connect with the vertices of the triangle intersect.

The line that contains the orthocenter in ΔABC is: line m.

What is the Centroid of a Triangle?

The centroid of a triangle is a the point of intersection where all three medians of a triangle. Medians of a triangle connects the vertices to the midpoints of the opposite sides of a triangle.

The line that contains the centroid in ΔABC is: line l.

What is the Incenter of a Triangle?

The incenter of a triangle is the point in a triangle where all three angle bisectors of the vertices of a triangle.

The line that contains the centroid in ΔABC is: line n.

Learn more about centers of a triangle on:

https://brainly.com/question/16045079

it's all i the picture help!! i don't remember how to solve it

Answers

I don’t know this but I need answers sorry

someone help pls pls

Answers

Answer:

3.636 hour. dividing 200miles /55m/h =3.636h

Answer:

3 hours 38 minutes is what calculators online say

Step-by-step explanation:

You should put both answers that were given to you. The answer on top seemed to do it the mathematical way youre suppose to. Maybe the teacher will take both answers i don’t know

4 out of the 10 employees at the sports shop are part-time employees. What percentage of the employees at the sports shop work part-time?

Write your answer using a percent sign (%).

Answers

Answer:

40%

Step-by-step explanation:

Well, if 4/10 work part time, 4/10 converted to percentages is 40%.

Lily has 7 fewer ribbons than Dora. Lily has 13 ribbons. How many ribbons does Dora have?

Answers

Answer: 6

Step-by-step explanation:

13-7=6

name all the properties of a square

Answers

Answer:

Here :)

Equilateral Polygon,

Convex Polygon,

Cyclic

Isgonal Figure

Istoxal Figure

helppp pleaseeeeee I don’t understand

Answers

Answer: x=32, y=45, z=45

Step-by-step explanation:

Now, x is cut in half on a flat plane which is a supplementary angle (2 angles that add up to 180 degrees) so just subtract 148 from 180 and you get 32.

Since a line cuts y and z equally in half and the line it is connected to is perpendicular (right angle), we can safely say both angles are equal to 45 degrees.

Krista's snow fort has an area of 6228 sq inches if it is 72 in long what is the width

Answers

Answer:

86.5 inches

Step-by-step explanation:

6228 / 72 = 86.5

The world population is about 7.8 billion people now and the population grows at an annual rate of 1.1%. What will the population be in 2031?

Answers

Answer:

8.58 billion people

Step-by-step explanation:

7.8

1.1

78

78

858 place the decimal where it should be to get 8.58

pls answer
a line has a slope of 19/9 and passes through the point (0,15). what is its equation in slope-intercept form?

Answers

Hey there!

We are given the slope of the line: 19/9.We are also given one of the points that the line passes through.Using this information, we can find the equation of the line.First, let's recall the Point-Slope formula:y-y1=m(x-x1)Plug in the given values:y-15=19/9(x-0)y-15=19/9xy=19/9x+15Therefore, the equation is: [tex]y=\frac{19}{9} x+15[/tex] :)

Hope this helps. Use the comment section to clarify your doubts.

Answered by

~A girl who helps others with a smile

#LetItSnow

Good luck.

If a truck leaves on Friday traveling 55 mph and is able to travel 10 hours per day, how many miles will it have driven after Monday?

Answers

it will have driven 550000 miles

Rosy went to the shoe store and counted 324 pairs of shoes. She went to another shoe store and counted 236 pairs. How many shoes did Rosy count in total.

Answers

Answer:

560

Step-by-step explanation:

Rosie counts 324 + 236 shoes

Let's start by separating each number into hundreds, tens, and ones

300, 20, 4

200, 30, 6

Then, we can add up each section

300 + 200 = 500

20 + 30 = 50

4 + 6 = 10

Finally, we can add up the sections

500 + 50 + 10 = 560

what is the sum of 4 and -5​

Answers

Answer:

-1

Step-by-step explanation:

its like subtracting 5 and 4

Solve the following equation algebraically: 3 x squared = 12 a. Plus-or-minus 3 b. Plus-or-minus 2 c. Plus-or-minus 3.5 d. Plus-or-minus 1.5

Answers

Answer:

b)  ±2

Step-by-step explanation:

3x² = 12

divide each side by 3 to get:

x² = 4

x = ±2

The value of the equation 3x² = 12 is x = ±2.

Option B is the correct answer.

What is an equation?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x = 6 is an equation.

We have,

3x² = 12

Divide 3 on both sides.

x² = 4

x = ±√4

x = ±2

Thus,

The value of x is  ±2.

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ2

Pointing to a photograph, a man said, "I have no brother, and that man's father is my father's son." Whose photograph was it?

Answers

The man’s son. Since the man has no brothers and the father of the man in the photograph is the man’s father’s son, the father of the man in the photograph must be the man. That means that the man in the photograph is the man’s son.

8:07, 8:58, ?, 10:43, 11:37
61
9:51
9:50
9:53
9:49

Answers

Answer:

  9:50

Step-by-step explanation:

It appears the sequence has 0:51 as the first difference, and those differences increase by 0:01 in each interval. That means ? must be chosen so that ...

  ? - 8:58 = 0:52   ⇒   ? = 8:58 +0:52 = 9:50

  10:43 -? = 0:53   ⇒   ? = 10:43 -0:53 = 9:50

The missing time is 9:50.

In the triangle below,
x = [ ? ] cm. Round to the
nearest tenth.
х
12 cm
170° 90°

Answers

Answer:

sine 70 = opposite / hypotenuse

sine 70 = 12 / x

x = 12 / sine 70

x = 12 / 0.93969

x = 12.7701688855 cm

x = 12.8 cm (rounded to nearest tenth.

Step-by-step explanation:

Please help me with this math problem!! NO LINKS PLEASE!! :)

Answers

Answer:

105°.

Step-by-step explanation:

1) to calculate m(∠ABC): m(∠ABC)=180-m(∠BAC)-m(∠(ACB)=180-90-65=25°;

2) note, m(∠ABC)=m∠(ABD)=25°, then it is possible

3) to calculate m(∠BAD): m(∠BAD)=180-m(∠ABD)-m(∠ADB)=180-25-50=105°.

Please help and quickly please and 20 points with brainelest




Thank you

Answers

Answer: The answer is B. 34

Step-by-step explanation:

3(12−9)+5^2

=(3)(3)+5^2

=9+5^2

=9+25

=34

Answer:

The answer is 34

Step-by-step explanation:

Order of operation is P.E.M.D.A.S. , or parenthesis, exponents, multiplication or division, then addition or subtraction.

3(12-9)+5²   Parenthesis3(3)+5²   Exponents3(3)+25   Multiplication9+25   Addition34   Answer

PLS HELP WILL MARK YOU BRAINLIEST!!
No fake answers pls

Answers

Answer:

1. =

Step-by-step explanation:

1.

R.H.S

5.2 + 5.a

(now taking 5 common)

5(2+a)

Sally can paint a room in 7 hours while it takes Steve 3 hours to paint the same room. How long would it take them to paint the room if they worked together?

Answers

Answer:

2 hours

Step-by-step explanation:

Answer:

2 hours

Step-by-step explanation:

Let x represent the time it takes together. Per hour the Equalizer

1/3hr + 1/8hr = 1/x  Multiplying each term by 24x so as all denominators = 1

8x + 3x = 24

11x = 24

x = 2.18 hrs, the time it takes them together

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