10. A large shipment of video streaming devices is accepted upon delivery if an inspection of 20 randomly selected video streaming devices yields no more than 1 defective item. a. Find the probability that the shipment is accepted if 3% of the total shipment is defective. b. Find the probability that the shipment is accepted if 15% of the total shipment is defective.

Answers

Answer 1

Answer:

a) 0.8802 = 88.02% probability that the shipment is accepted

b) 0.1756 = 17.56% probability that the shipment is accepted if 15% of the total shipment is defective.

Step-by-step explanation:

For each item, there are only two possible outcomes. Either it is defective, or it is not. The probability of an item being defective is independent of any other item. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

20 randomly selected video streaming devices

This means that [tex]n = 20[/tex]

a. Find the probability that the shipment is accepted if 3% of the total shipment is defective.

3% defective means that [tex]p = 0.03[/tex]

Probability of at most 1 defective is:

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

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{20,0}.(0.03)^{0}.(0.97)^{20} = 0.5438[/tex]

[tex]P(X = 1) = C_{20,1}.(0.03)^{1}.(0.97)^{19} = 0.3364[/tex]

[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.5438 + 0.3364 = 0.8802[/tex]

0.8802 = 88.02% probability that the shipment is accepted.

b. Find the probability that the shipment is accepted if 15% of the total shipment is defective

Now [tex]p = 0.15[/tex]. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{20,0}.(0.15)^{0}.(0.85)^{20} = 0.0388[/tex]

[tex]P(X = 1) = C_{20,1}.(0.15)^{1}.(0.85)^{19} = 0.1368[/tex]

[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.0388 + 0.1368 = 0.1756[/tex]

0.1756 = 17.56% probability that the shipment is accepted if 15% of the total shipment is defective.


Related Questions

What is the product of (t – 4) (t? + 2t - 6)?

Answers

Answer:

Step-by-step explanation:

(t - 4) (t + 2t - 6)

= t2 + 2t2 - 6t - 4t - 6t + 24

= Solving like terms

= 3t2 - 16t + 24

What is the quotient when (x+ 2) is divided into the polynomial 2x2 - 2x - 12?
O A. 2x-5 with no remainder
O B. X+ 3 with a remainder of -2
O C. 2x-3 with a remainder of 5
O D. 2x-6 with no remainder

Answers

Answer:

2x² - 2x - 12 ÷ (x+2)

= 2x - 6

D. 2x-6 with no remainder

The quotient when (x + 2) is divided into the polynomial 2x² - 2x - 12 is, (2x - 6) with no remainder.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

To find the quotient when (x + 2) is divided into the polynomial

2x² - 2x - 12.

Now,

The polynomial is,

⇒ 2x² - 2x - 12

⇒ 2 (x² - x - 6)

⇒ 2 (x² - 3x + 2x - 6)

⇒ 2 [ x (x - 3) + 2(x - 3) ]

⇒ 2 [ (x + 2) (x - 3) ]

Hence, We can divide polynomial by (x + 2) as;

⇒ 2 [ (x + 2) (x - 3) ] ÷ (x + 2)

⇒ 2 (x - 3)

⇒ 2x - 6

Therefore, the quotient when (x + 2) is divided into the polynomial

2x² - 2x - 12 is, (2x - 6) with no remainder.

Learn more about the divide visit:

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In Exercises 1-4, the sample size n, probability of success p, and probability of
failure q are given for a binomial experiment. Determine whether you can use a
normal distribution to approximate the distribution of x.
1. n = 24, p = 0.85, 9 = 0.15
2. n = 15, p = 0.70, q = 0.30
3. n = 18, p = 0.90, q = 0.10
4. n = 20, p = 0.65, q = 0.35

Answers

Answer:

1. No

2. No

3. No

4. Yes

Step-by-step explanation:

Binomial approximation to normal.

The binomial probability distribution has parameters n, p and q.

If

[tex]np \geq 5[/tex] and [tex]nq \geq 5[/tex], you can use the normal approximation.

1. n = 24, p = 0.85, q = 0.15

[tex]np = 24*0.85 = 20.4 > 5[/tex]

[tex]nq = 24*0.15 = 3.6 < 5[/tex]

So no.

2. n = 15, p = 0.70, q = 0.30

[tex]np = 15*0.7 = 10.5 > 5[/tex]

[tex]nq = 15*0.3 = 4.5 < 5[/tex]

So no.

3. n = 18, p = 0.90, q = 0.10

[tex]np = 18*0.9 = 16.2 > 5[/tex]

[tex]nq = 18*0.1 = 1.8 < 5[/tex]

No

4. n = 20, p = 0.65, q = 0.35

[tex]np = 20*0.65 = 13 > 5[/tex]

[tex]nq = 20*0.35 = 7 > 5[/tex]

Yes

The figure shows a pentagon. The length of each side is given
as shown. Find the perimeter of the pentagon in terms of w.
Please help !!




Answers

Answer:

perimeter = sum of all side

perimeter in terms of w= w+w+w+w+w

i.e= 5w

Quick for 15 points. William was playing a board game that had a spinner with six equal-sized sections. Three of
the sections were red, two sections were blue, and one section was yellow. Find the probability
that he landed on a purple section.
Ratio:
Percent:

Answers

Ummmmmm u didn’t say how many parts were purple but I’m assuming there’s one so

1/6= 6:1 (ratios)

1/6= 16.666666666(it goes on forever)

Not sure if it’s correct or not so u might wanna double check ur answer

In ΔIJK, the measure of ∠K=90°, KJ = 63, IK = 16, and JI = 65. What ratio represents the sine of ∠I?

Answers

The sine of ∠I is represented by the ratio 63:65

Devonte is 7 years older than Hanna. In 7 years the sum of their ages will be 83. How old is Devonte now?

Answers

Answer:

Hannah = 34 and 1/2

Devonte = 41 and 1/2

Step-by-step explanation:

Hanna = x

Devonte = x+7

x+x+7=83-7

2x+7=76

2x=76-7

2x=69

x=34.5

Hannah = x = 34.5

Devonte = x+7 = 41.5

which models represent 1/4÷6 choose all correct answers​

Answers

Answer:

[tex]\dfrac{1}{24}[/tex]

Step-by-step explanation:

We need to find the value of 1/4÷6.

It can be done as follows :

[tex]\dfrac{\dfrac{1}{4}}{6}[/tex]

We know that, [tex]\dfrac{\dfrac{1}{x}}{y}=\dfrac{1}{xy}[/tex]

We have, x = 4 and y = 6

So,

[tex]\dfrac{\dfrac{1}{4}}{6}=\dfrac{1}{4\times 6}\\\\=\dfrac{1}{24}[/tex]

So, the final answer is equal to [tex]\dfrac{1}{24}[/tex].

Find the volume of the sphere. Radius is 1

Answers

Hi there!

[tex]\large\boxed{V = 4/3\pi \text{ or } \approx 4.19 \text{ } units^{3}}[/tex]

Find the volume of a sphere using the following equation:

V = 4/3πr³

Substitute in the given radius:

V = 4/3π(1)³

V = 4/3π or ≈ 4.19 units³

Answer:

32/3π on khan academy

Step-by-step explanation:


What is the area of the square? It has a side of 5 mm.

Please help i give brainliest

Answers

Answer:
25



Exp: bh so 5x5

Which expression is equivalent to -6(3 + 4x)?

Answers

Answer:

A

Step-by-step explanation:

may I have brainllest

Answer:

A

Step-by-step explanation:

What is the volume? 3 m 1 m cubic meters​

Answers

Answer:

9 cubic meters

Step-by-step explanation:

V = lwh

V = 1 by 3 by 3

Answer:

9 cubic meters

Step-by-step explanation:

1x3x3=9

Where is Point A located on the coordinate grid?

Answers

Answer:

Quadrant 11

Step-by-step explanation:

Quadrant 2 mark as brainllest

When I solved this quadratic using the square root property, I am not sure if i did it correctly and I am not sure if there should be two x solutions.

Answers

Answer:

yup your answer is right

Step-by-step explanation:

two x solutions are +2√3

+2√3 can be written as +2√3 or -2√3

Answer:

yesssss you are rightttt

A picture of Margo's garden is shown below. It is made of 2 rectangular prisms. She wants to
-10 feet -
1 foot
3 feet
7 feet
3 feet
7 feet
2 feet
09 cubic feet
O 10 cubic feet
0 98 cubic feet
0 107 cubic feet

Answers

The Volume of dirt required for the Margo's garden which is made of 2 rectangular prisms is, 107 cubic feet, So option D is correct

What is Volume?

In mathematics, Space occupied by three dimensional objects is called Volume. Basically it is a space within closed region of  every three dimensional objects.

In given problem, we have two rectangular prisms

One has sides (1 feet, 3  feet, 3  feet)

Another one has sides (2 feet, 7 feet, 7 feet)

Volume of a rectangular prism  = Length×Height×Width

Volume of a rectangular prism 1  = 3×1×3 = 9

Volume of a rectangular prism 2  = 7×2×7 = 98

Total Volume = 107

Hence, Total dirt required  107 cubic feet

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How do you do the half and sum of the equation?​

Answers

Answer:

13x - 4

Step-by-step explanation:

Hi,

5(3x -1)

-1/2(4x - 2)

To add...

5(3x - 1) + -1/2(4x - 2)

15x - 5 - 2x + 1

13x - 4

That's your answer :)

I hope this helps!

What is the value of X PLEASE HLEPPP

Answers

Answer:

Using the formula,(x= base×height).

And the formula, (6+6×).

The answer should be: (A) 12

Step-by-step explanation:

Hope this helps! Have a good day/or night!

P.S: Sorry if I'm wrong I tried my best. Best wishes!!! And here's some sparkles ✨ (◍•ᴗ•◍)✧*。!!!

The value of x would be A (12)

Select which correctly describe the 92% confidence interval. (Select all that apply.)

a. We are 92% confident that the mean height of the entire business is larger than this interval.
b. The upper height represents the 92nd percentile.
c. We are 92% confident that the mean height of the entire business is in this interval.
d. The 92% confidence interval is a subset of the 85% confidence interval.
e. We are 8% confident that the mean height of the entire business is in this interval.
f. The 85% confidence interval is a subset of the 92% confidence interval.
d. 92 employees have heights in this interval.
e. 92% of employees have heights in this interval.

Answers

Answer:

c. We are 92% confident that the mean height of the entire business is in this interval.

f. The 85% confidence interval is a subset of the 92% confidence interval.

Step-by-step explanation:

x% confidence interval:

A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b.

Margin of error:

The larger the confidence interval, the larger the margin of error. That means that for example, an 85% confidence interval is a subset of the 92% confidence interval.

In this question:

92% confidence interval -> We are 92% sure that the population mean is in this interval.

The 85% confidence interval is a subset of the 92% confidence interval.

So options c and f.

Please help! Picture attached!

Answers

Answer:

6.2

Step-by-step explanation:

Formula :

Distance between two points = √(xB−xA)2+(yB−yA)2(xB-xA)2+(yB-yA)2

Solution :

Distance between two points = √(5.5−1)2+(9.25−5)2(5.5-1)2+(9.25-5)2

= √4.52+4.2524.52+4.252

= √20.25+18.062520.25+18.0625

= √38.312538.3125 = 6.1897

What is the approximate value of this logarithmic expression?

Answers

9514 1404 393

Answer:

  B.  1.80

Step-by-step explanation:

The change of base formula can be used.

  [tex]\log_5(18)=\dfrac{\log{18}}{\log{5}}\approx\dfrac{1.25527}{0.69897}\approx1.7959\\\\\boxed{\log_5{18}\approx1.80}[/tex]

_____

Some calculators can compute the value for you directly.

Kaitlyn is walking on a treadmill at a constant pace for 28 minutes. She has programmed the treadmill for a 2-mile walk. The display counts backward to show the distance remaining. Enter and graph the equation that gives the distance f(x) left in miles as a function of the number x of minutes she has been walking. Then, find and compete the interpretation of the x- and y-intercepts.

Answers

Is this multiplying or what??? Anyways try calculating those numbers so basically you need to calculate 28x2 or if you have to divide them or multiply them you would get the answer is very simple

Compare the graph of g(x) = 6x2 with the graph of f(x) = x2.

Answers

Answer:

see explanation

Explanation:

the graph of g(x) is the graph of f(x) shifted vertically by

+ 6 units

or equivalent to a translation  

(

0

6

)

in general  

g

(

x

)

=

x

2

±

a

for  

a

>

0

shift is  

(

0

a

)

for  

a

<

0

shift is  

(

0

a

)

graph{(y-x^2)(y-x^2-6)=0 [-20, 20, -10, 10]}

Step-by-step explanation:

Find the value of x

Answers

Answer: 38

Step-by-step explanation:

Brainlest and points !! Picture included

Answers

Itssssssss 30 have a nice day

Clara bought 16 cases of water bottles. There were 12 water bottles in each case. Four students wrote and solved equations to find b, the number of bottles that Clara bought. Which student wrote and solved the equation correctly?
Maya’s work:
StartFraction b Over 12 EndFraction = 16. b = 1.3
Larissa’s work:
12 b = 16. b = 1.3
Sally’s work:
StartFraction b Over 12 EndFraction = 16. b = 192.
Anika’s work:StartFraction 12 Over b EndFraction = 16. b = 192.

Answers

Answer:

Sally is correct

Step-by-step explanation:

[tex]\frac{b}{12} =16[/tex]

to solve for b we can multiply both sides by 12 to get b alone.

b = 16 × 12

b = 192

Add the product of 2 and 5 to the product of 9 and 8

Answers

Answer:

82

Step-by-step explanation:

2*5 + 9*8 = 10 + 72 = 82

Answer:

82

Step-by-step explanation:

product means multiply 2*5= 10  9*8= 72

10 + 72 = 82

A sixty-minute television program has 5 commercial breaks. Each break lasts 2 minutes. Write a numerical expression that represents the length of the program without commercial breaks. *

Answers

Answer: 60 - 10

Step-by-step explanation:

There are 5 commercial breaks with each of the breaks lasting 2 minutes.

Commercial breaks in total therefore last:

= 5 * 2

= 10 minutes.

The program is a 60 minute program so to find the amount of time the program lasts without the commercials, the expression is:

= 60 - 10

It lasts 50 minutes without commercials.

An atom of gold has a mass of approximately 3.25 x 10-22 grams. What is the mass of
7000 atoms of gold? Express your answer in scientific notation.

Answers

3.25 would Raquel to 47 so 20

If , p x 6= 36 what is p? A. 1/6 B. 6 C. 216 D. 180

PLEASSEEEEEE

Answers

Answer:

6

Step-by-step explanation:

All you need to do is the inverse operation: 36 divided by 6, which is 6!

Pleaseeee helpp which one is it and whyyyy!!!!

Answers

Answer:

answer is A

Step-by-step explanation:

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