Question Help When purchasing bulk orders of​ batteries, a toy manufacturer uses this acceptance sampling​ plan: Randomly select and test 36 batteries and determine whether each is within specifications. The entire shipment is accepted if at most 2 batteries do not meet specifications. A shipment contains 3000 ​batteries, and 3​% of them do not meet specifications. What is the probability that this whole shipment will be​ accepted? Will almost all such shipments be​ accepted, or will many be​ rejected?

Answers

Answer 1

Answer:

The probability is [tex]P(X  \le 2 ) = 0.9072[/tex]

The company will accept 90.72% of the shipment and will reject [tex](100 -90.72) =  9.2\%[/tex] of the shipment , so many of the shipment are rejected

Step-by-step explanation:

From the question we are told that

   The  sample size is  n =  36

   The  proportion that did not meet the requirement is  [tex]p =  0.03[/tex]

Generally the probability that the whole shipment is accepted is equivalent to the probability that there is at most 2 batteries that do not meet the requirement , this is mathematically represented as

     [tex]P(X  \le 2 ) = [ P(X =  0 ) +  P(X =  1 ) + P(X = 0)][/tex]

=>   [tex]P(X  \le 2 ) = [ [^{n}C_0 * (p)^{0} *(1-p)^{n-0} ] +  [^{n}C_1 * (p)^{1} *(1-p)^{n-1} ] +  [^{n}C_2 * (p)^{2} *(1-p)^{n-2} ]][/tex]

Here C stands for Combination (so we will be making the combination function in our  calculators )

So

=> [tex]P(X  \le 2 ) = [ [^{36}C_0 * (0.03)^{0} *(1-0.03)^{36-0} ] +  [^{36}C_1 * (0.03)^{1} *(1-0.03)^{36-1} ] +  [^{36}C_2 * (0.03)^{2} *(1-0.03)^{36-2} ]][/tex]

=> [tex]P(X  \le 2 ) = [ [1 * 1 * 0.3340  ] +  [36* 0.03 *0.3444 ] +  [630 * 0.0009 *(0.355 ]][/tex]

=>[tex]P(X  \le 2 ) = 0.9072[/tex]

The company will accept 90.72% of the shipment and will reject [tex](100 -90.72) =  9.2\%[/tex] of the shipment , so many of the shipment are rejected

 


Related Questions

PRACTICE ANOTHER Is 4a a factor of 2a · 38b? (Assume that a and b represent integers.) Yes, because 4 is a multiple of 38. Yes, because 2a · 38b = 4a · 19b where 4a and 19b are integers because a and b are integers and products of integers are integers. Yes, because 4a is a divisor of 38b. No, because 38 is not a divisor of 4. No, because 2a · 38b = 4a · 19b where 4a and 19b are not necessarily integers because products of integers are not always integers.

Answers

Answer:

Yes, [tex]2a . 38b = 4a . 19b[/tex]

Step-by-step explanation:

Given

[tex]Expression: 2a.38b[/tex]

Required

Is 4a a factor of the expression?

Analyzing each option.

1.

[tex]2a . 38b = 4a . 19b[/tex]

[tex]76ab = 76ab[/tex]

The above expression is true.

Hence: This option answers the question

For a certain type of sand, 1 cubic foot weighs 80 pounds. The sand goes in a container that weighs 40 pounds. Use the Ray tool to make a graph that shows the total weight of the container and sand, w, filled with n cubic feet of this sand. I need the coordinates for the graph please.

Answers

Answer:

First, let's write our equation in a general way.

We know that:

1 cubic foot weighs 80 pounds.

The container weighs 40 pounds.

Then, if i put n cubic feet of sand in the container, the total mass will be one time the mass of the container plus n times the mass of one cubic foot of sand.

We can write this as:

w(n) = 40lb + n*80lb

This is a linear equation, where the y-axis will represent the mass in pounds and the x-axis will be the number of cubic feet of sand in the container in units, a graph of this is shown below.

You can see that it is really steep, this is because for really small increments in n, the weight increases a lot.

Answer

ok, Just plot the points at (0,40) and (2,200) :))

Sophia says that you can solve the problem in the Example by multiplying both quantities in the ratio 60:36 by one-sixth. Is Sophia correct?

Answers

Answer:

Sophia is not correct

Step-by-step explanation:

The given situation represent the problem of a ratio and it is predicted to do the simplify the ratio by determining the smallest possible values

Here it can be presented 60:36 as a fraction i.e. [tex]\frac{60}{36}[/tex]

Now the fraction should be fall by dividing both the numerator and denominator by a common factor i.e. 6

Now after dividing it, the fraction would be [tex]\frac{10}{6}[/tex]

Now it can be further reduced by a common factor i.e. 2

So now the fraction is [tex]\frac{5}{2}[/tex]

Thus, the ratio is 5:2

Hence, she is not correct

A backpack costs $18 and has a 7 percent tax. How much will Sheila have to pay for the backpack after tax?
O $1.26
O $5.40
O $19.26
O $30.60

Answers

Answer:

1

Step-by-step explanation:

1.26

19.26. Do not forget to add your backpacks cost to the tax. You can take 18 dollars times 1.07 to get the tax and add the tax to the 18. Hope that helps!

Before adding the following fractions, you need to find the common ? 2/3 + 1/6 =

Answers

Answer:

denominator

Step-by-step explanation:

Answer:

5/6

Step-by-step explanation:

2/3×2/2 + 1/6

4/6 + 1/6

5/6

Jade used 3/4
yard of fabric to make a scart. Can she make 2 of these scarves with 1 4/5 yards of fabric, and why?

Answers

Answer:

Yes she can

Step-by-step explanation:

3/4 = 0.75

1 4/5= 1.8

0.75 x 2 = 1.5 which is less that 1.8 so she can

6 - 8x = 6x - 9x + 11

Answers

6-8x=-3x+11

-8x+3x=11-6

-5x=5

x=-1

The first step is to isolate the variable, then you solve. Hope this helps, brainliest if you can.

Answer:

hi

Step-by-step explanation:

hi i am a gamergirl add me in fortnite xxgamergilxx93_qt

It too Mrs. phillips 1.6 hours to run the 13.2 miles. What was his average speed

Answers

Answer:

13.2 miles/ 1.6 hours= 8.25 miles/hour.Mr. Phillips's speed was 8.25

There are 100 students at a school and three dormitories A, B, and C with capacities of 25, 35, and 40, respectively.

Required:
a. How many ways are there to fill up the dormitories?
b. Suppose that, of the 100 students, 50 are men and 50 arewomen and that A is an all-men's dorm, B is an all-women's dorm andC is co-ed. How many ways are there to fill thedormitories?

Answers

Answer:

a

[tex]N = 7.0 *10^{44} \ Ways [/tex]

b

[tex]U  = 2.85 *10^{26}\  ways [/tex]

Step-by-step explanation:

From the question we are told that

   The number of students are  n =  100

    The number of dormitories  is  k =  3

    The capacity of the first dormitory is  A =  25

     The capacity of the second dormitory is  B =  35

      The capacity of the third dormitory is  c =  40

Generally the number of way to fill the dormitory up is mathematically represented as

      [tex]N  =  \frac{n!}{A! B!C!}[/tex]

=>   [tex]N  =  \frac{100!}{25! 35! 40!}[/tex]

Here ! stands for factorial, so we will be making use of the factorial functionality in our calculators to  evaluated the above equation

=>   [tex]N  =  \frac{100!}{25! 35! 40!}[/tex]

[tex]N = \frac{9.332622* 10^{157}}{[1.551121* 10^{25}]* [1.0333148* 10^{40}] * [8.1591528*10^{47}]}[/tex]

[tex]N = 7.0 *10^{44} \ Ways [/tex]

From the question we are told that there are 50 men and  50  women and

     A is  all-men's dorm and  B is all-women's dorm while C is co-ed

So

When A is filled , the number of men that will be remaining to fill dorm C is  50-25 = 25

While when B is filled the number of women that will be remaining to fill dorm C is   50-35 = 15

Generally the number of ways there to fill the dormitories is equivalent to the number of ways of selecting the 25 men and 35 women to fill dormitory A and B plus one more way which is filling dorm C with the remaining students this is  mathematically represented as  

       [tex]U  =  ^{50}C_{35} * ^{50}C_{25}  +  1[/tex]

Here C stands for combination hence we will be making use of the combination functionality in our calculators

     [tex]U  = 2.250829575* ^{12}  * 1.264106064 * 10^{14} +  1[/tex]

=>    [tex]U  = 2.85 *10^{26}\  ways [/tex]

     

Find the value of x.

Please help!!​

Answers

X is equal to 5. Hope this helps and have a good day. Also, A Brainliest would be much appreciated

Answer:

5

Step-by-step explanation:

Use the Exterior Angle Theorem.

The E.A.T states that the measurement of an exterior angle is found by adding the two opposite and non-adjacent interior angles.

In this case, the Exterior Angle is 121. The sum can be found by combining 17x - 4 and 8x. Set the equation:

17x - 4 + 8x = 121

First, combine like terms:

17x + 8x - 4 = 121

(17x + 8x) - 4 = 121

(25x) - 4 = 121

Next, Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

First, add 4 to both sides of the equation:

25x - 4 (+4) = 121 (+4)

25x = 121 + 4

25x = 125

Next, divide 25 from both sides:

(25x)/25 = (125)/25

x = 125/25

x = 5

5 is your value for x.

~

A diver swims 5.875 feet up to the surface of the water. Which number represents the diver’s position in relation to the surface before swimming to the top?
-5.9 feet
Negative 5 and three-fourthsfeet
-58 feet
Negative 5 and StartFraction 7 over 8 EndFractionfeet

Answers

Answer:

Negative 5 and 7 over 8

Step-by-step explanation:

Answer:

Negative 5 and StartFraction 7 over 8

Step-by-step explanation:

Wade picked 4 pints of blackberries. His friend, Matt, picked 6 pints. How
many pints did they pick altogether?

Answers

Together they picked 10 pints of blackberries.
10 pints in all , 4+6=10

A farm has 56 horses and sheep in all. There are 8 fewer sheep than horses. How many horses are there on the farm?

Answers

Answer:

32 Horses

Step-by-step explanation:

32-8=24

There are 32 horses and 24 sheep (As you can see there are 8 fewer sheep than horses)

I sort of guess and checked:

I tried to think of 2 numbers that added to 56 but one number was 8 less than the other one.I figured out that 32 and 24 fit this description :)

Riley and Rhoda plan to buy several bags of dog food and a dog collar. Each bag of dog food costs $7, and the dog collar cost $5

Answers

Answer:

2bags= $14 + $5

3bags= $21+ $5

4bags= $28 + $5

5bags= $35 + $5

6bags= $42 + $5

multiply # of bags by 7

and add $5

translate the sentence into an equation

The sum of 6 times a number and 2 is equal to 3

Answers

Answer:

6x + 2 = 3

Step-by-step explanation:

x would represent the unknown number

The sum refers to addition

6 times a number would be 6x (you can use any variable, but for this example I'm using x)

When you put it all together, it is 6x + 2 = 3

The required equation is 6x + 2 = 3.

It is required to find the equation.

What is equation?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers

Given:

The sum of 6 times a number and 2 equals 3.

According to given question we have,

Let the number be x.

6 times a number would be

6x

The sum of 6 times a number and 2 equals 3.

6x + 2 = 3.

Therefore, the required equation is 6x + 2 = 3.

Learn more about equation here:

brainly.com/question/18760193

#SPJ2

Help please thanks :)

Answers

Answer:

the answer is part 3 : exactly 30 .....

The answer 3 : exactly 30..

How many days are in 5 years? Correct answer gets brainliest. 2 possible answers

Answers

Answer:

1826.21099

Step-by-step explanation:

Answer: 1825 days.

Step-by-step explanation: 365x5=1825

Four times the sum of f and g is identical to six times g

Answers

Answer:

4(f+g)=6g

Step-by-step explanation:

4(f+g)=6g

Simplify 2x^3 х 3x^2 ​

Answers

Answer:

ans = 6x4

Step-by-step explanation:

(2x2)(3x2)

first multiply the coefficients

(2*3) = 6

next multiply the variables

(x2*x2) = x2+2 = x4

productofcoeficients,productofvariables

= 6x4

f(x) = 2x^3 g(x) = x-3

find f(2)
find g(4)
find (f+g) (x)

Answers

[tex]f(x) = 2 {x}^{3} [/tex]

[tex]f(2) = 2 \times {2}^{3} = 2 \times 8 = 16 [/tex]

_________________________________

[tex]g(x) = x - 3[/tex]

[tex]g(4) = 4 - 3 = 1[/tex]

_________________________________

[tex](f + g)(x) = f(x) + g(x) [/tex]

[tex](f + g)(x) = 2 {x}^{3} + x - 3 [/tex]

_________________________________

Done...♥️♥️♥️♥️♥️


Emilia wrote a total of 12 pages over 4 hours. After spending 6 hours writing this week, how
many pages will Emilia have written in total? Assume the relationship is directly proportional.

Answers

Answer:

30 pages

Step-by-step explanation:

Knowing she wrote 12 pages in 4 hours, we can do 12/4 to get 3 pages per hour. Multiply 3 pages by the 6 hours she spends writing and you get 18 pages in 6 hours. Add 12 pages and 18 pages and you have 30 pages.

If 5% more than a is b, and b is 15% less than, what is the ratio of a to c? Please answer quickly.

Answers

You didn’t show the full question/picture

PLEASE HELP!!


Sorry for all the tabes I'm working on a presentation at the same time.

Answers

Answer:

0.5

Step-by-step explanation:

use rise over run, from (-6,0) to (0,3) it rises 3 and runs 6. 3/6 = 1/2.

Answer:

the slope is two

Step-by-step explanation:

rise over run

M is the midpoint of line segment PQ. MQ = 5x + 8 and PQ = 6x + 65, find x

Answers

Answer:

freeeeeeeeeeeeeeeeeeeeeeeee

Step-by-step explanation:

trump 20202020202020020202020

A nursery owner buys 8 panes of glass to fix some damage to his greenhouse. The 8 panes cost
$19.60. Unfortunately, he breaks 3 more panes while repairing the damage. What is the cost of
another 3 panes of glass?
Another 3 panes of glass cost $

Answers

Answer:

$8.85

Step-by-step explanation:

Step-by-step explanation: well if you take 23.60 and divide it by 8 you would get 2.95 times that by three and you would get 8.85 and there's your answer.

Answer:

7.35    

because my kid got the question wrong              

7th grade math help me plzzz

Answers

Answer:

11.a) is 15+5.50+3 maybe

11.b) is $3.50 because 15-12=3 3+5.50=8.50 8.50+3=11.50 11.50-8=3.50

The sum of 48 and itself, its half and half of the half is added to 18.​

Answers

Answer:

150

Step-by-step explanation:

This is a word problem which should be tackled accordingly.

The sum of 48 and itself

= 48+48

= 96

It's half and half of its half

= 48/2 and (48/2)/2

= 24+ 24/2

= 24+12

= 36

Is added to 18

= 96+36+18

= 150

From the description above the entire sum is 150.

Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanations. The distribution of pH levels for all community swimming pools in a large county is approximately normal with mean 7.5 and standard deviation 0.2. According to swimming pool studies, the safest pH levels for water in swimming pools are between 7.2 and 7.8. (a) One community swimming pool in the county will be selected at random. What is the probability that the selected pool has a pH level that is not considered safe

Answers

Answer:

The  value is  [tex]P(A) =  0.133617[/tex]

Step-by-step explanation:

From the question we are told that

  The  mean is  [tex]\mu =  7.5[/tex]

  The standard deviation is  [tex]\sigma  =  0.2[/tex]

  The safest water level is  between  7.2 and  7.8

Generally the probability that the selected pool has a pH level that is not considered safe is mathematically represented as

       [tex]P(A) =  1 - P(7.2 \le X  \le 7.8 )[/tex]

Here  

      [tex]P(7.2 < X  < 7.8 ) = P(\frac{ 7.2 - \mu }{\sigma } <  \frac{X - \mu }{ \sigma } <\frac{ 7.8 - \mu }{\sigma }   )[/tex]

Generally [tex]\frac{X - \mu }{ \sigma } =  Z (The  \ standardized \  value  \  of  X )[/tex]

So

 [tex]P(7.2 < X  < 7.8 ) = P(\frac{ 7.2 - 7.5 }{0.2 } < Z <\frac{ 7.8 - 7.5 }{0.2 }   )[/tex]    

 [tex]P(7.2 < X  < 7.8 ) = P(-1.5 < Z <1.5)[/tex]  

=>  [tex]P(7.2 < X  < 7.8 ) = P(Z <  1.5) - P(  Z < - 1.5) [/tex]

From the z-table the probability of  (Z <  -1.5) and   (  Z <1.5)  are

    [tex]P(Z <  1.5) =  0.93319[/tex]

and  

    [tex]P(Z <  -1.5) =  0.066807[/tex]

So

      [tex]P(7.2 < X  < 7.8 ) =0.93319 - 0.066807 [/tex]

       [tex]P(7.2 < X  < 7.8 ) =0.0866383[/tex]

So

   [tex]P(A) =  1 - 0.0866383[/tex]

=>  [tex]P(A) =  0.133617[/tex]

The probability that the selected pool has a pH level that is not considered safe pool is 0.1336

The given parameters are:

[tex]\mathbf{\mu = 7.5}[/tex]

[tex]\mathbf{\sigma = 0.2}[/tex]

Start by calculating the probability that a pool is safe.

This is represented as: P(7.2 < x < 7.8)

Calculate the z-scores for x =7.2 and 7.8 using:

[tex]\mathbf{z = \frac{x - \mu}{\sigma}}[/tex]

So, we have:

[tex]\mathbf{z = \frac{7.2 - 7.5}{0.2} = -1.5}[/tex]

[tex]\mathbf{z = \frac{7.8 - 7.5}{0.2} = 1.5}[/tex]

So, we have:

[tex]\mathbf{P(7.2 < x < 7.8) = P(-1.5 < z < 1.5)}[/tex]

This gives

[tex]\mathbf{P(7.2 < x < 7.8) = P(z < 1.5) - P(z < -1.5)}[/tex]

Using z table of probabilities, we have:

[tex]\mathbf{P(7.2 < x < 7.8) =0.9332 - 0.0668}[/tex]

[tex]\mathbf{P(7.2 < x < 7.8) =0.8664}[/tex]

The probability that the pool is not safe is calculated using the following complement formula

[tex]\mathbf{P(Not\ Safe) = 1 - P(Safe)}[/tex]

So, we have:

[tex]\mathbf{P(Not\ Safe) = 1 -0.8664}[/tex]

[tex]\mathbf{P(Not\ Safe) = 0.1336}[/tex]

Hence, the probability that the pool is not safe is 0.1336

Read more about probabilities at:

https://brainly.com/question/11234923

Shirley is drawing triangles that have the same area. The base of each
triangle varies inversely with the height. What are the possible base
and height of a second triangle if the first triangle's base is 12 and its
height is 8?
Select one:
a. 120 and 80
b. 10 and 10
c. 60 and 36
d. 16 and 6

Answers

Answer:

d. 16 and 6

Step-by-step explanation:

Triangle area = (base × height)/2

A = (8 × 12)/2 = 96/2 = 48

A = (16 × 6)/2 = 96/2 = 48

what ratio is lesa than 7/15​

Answers

Answer:

2/5=6/15 and that is less so....

Step-by-step explanation:

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