The average defect rate on a 2010 Volkswagen vehicle was reported to be 1.33 defects per vehicle. Suppose that we inspect 100 Volkswagen vehicles at random. (a) What is the approximate probability of finding at least 157 defects

Answers

Answer 1

Answer:

0.0207 = 2.07% approximate probability of finding at least 157 defects

Step-by-step explanation:

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\lambda[/tex] is the mean in the given interval.

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 z-score 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 p-value, we get the probability that the value of the measure is greater than X.

n instances of a Poisson distribution can be approximated to a normal distribution, with [tex]\mu = n\lambda, \sigma = \sqrt{\lambda}\sqrt{n}[/tex]

The average defect rate on a 2010 Volkswagen vehicle was reported to be 1.33 defects per vehicle.

This means that [tex]\lambda = 1.33[/tex]

Suppose that we inspect 100 Volkswagen vehicles at random.

This means that [tex]n = 100[/tex]

Mean and standard deviation:

[tex]\mu = n\lambda = 100*1.33 = 133[/tex]

[tex]\sigma = \sqrt{\lambda}\sqrt{n} = \sqrt{1.33}\sqrt{100} = 11.53[/tex]

What is the approximate probability of finding at least 157 defects?

Using continuity correction(Poisson is a discrete distribution, normal continuous), this is [tex]P(X \geq 157 - 0.5) = P(X \geq 156.5)[/tex], which is 1 subtracted by the p-value of Z when X = 156.5. So

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

[tex]Z = \frac{156.5 - 133}{11.53}[/tex]

[tex]Z = 2.04[/tex]

[tex]Z = 2.04[/tex] has a p-value of 0.9793.

1 - 0.9793 = 0.0207

0.0207 = 2.07% approximate probability of finding at least 157 defects


Related Questions

Which graph represents the given equation? y=3/2x^2+4x-2

Answers

Answer:

y=3/2x^2+4x-2

Hope it helps

Please answer and explain :)
Write an example for each of the following:
equation notation
set notation
interval notation
solution graph

Answers

Answer:

set notation _ A set is denoted or represented by a capital letter and enclosed in a curly bracket For example {A,B,P,Q}.

May I get help with this question?

Answers

Answer:

C. <F

Step-by-step explanation:

The angle that sees the largest side length has the largest measurement.

Amongst the given side lengths the one that sees <F has the longest length so the answer is C

3/4 of the households in a rural area have pets. how many households have pets in this area if there are 1500 total households

Answers

Answer:

1,125 households would have pets in the area.

Step-by-step explanation:

We have 1,500 total households. We also know that 3/4 (or 0.75) of these households have pets. We would multiply 1,500 by 0.75 (which is equal to 3/4), resulting in 1,125. Therefore, 1,125 households would have pets in the area.

Answer:

1125 households

Step-by-step explanation:

3/4 of total households in area = # of households that have pets in the area

3/4 of 1500 = # of households that have pets in the area

3/4 · 1500 = # of households that have pets in the area

75/100 · 1500 = # of households that have pets in the area

0.75 · 1500 = 1125

1125 households

Graph the function g(x) = 3^x + 3 and give its domain and range using interval notation.

Answers

When a function is plotted on a graph, the domain and the range of the function are the x-coordinate and the y-coordinate respectively.

The domain and the range of the given function are:

Domain: [tex](-\infty,\infty)[/tex]

Range: [tex](3,\infty)[/tex]

 The given function is:

[tex]g(x) = 3^x + 3[/tex]

First, we plot the graph of g(x)

To do this, we need to generate values for x and g(x). The table is generated as follows:

[tex]x = 0 \to g(0) = 3^0 + 3 = 4[/tex]

[tex]x = 1 \to g(1) = 3^1 + 3 = 6[/tex]

[tex]x = 2 \to g(2) = 3^2 + 3 = 12[/tex]

[tex]x = 3 \to g(3) = 3^3 + 3 = 30[/tex]

[tex]x = 4 \to g(4) = 3^4 + 3 = 84[/tex]

The generated values in tabular form are:

[tex]\begin{array}{cccccc}x & {0} & {1} & {2} & {3} & {4} \ \\ g(x) & {4} & {6} & {12} & {30} & {84} \ \end{array}[/tex]

Refer to the attached image for graph of g(x)

To determine the domain, we simply observe the x-axis.

The curve stretches through the x-axis, and there are no visible endpoints on the axis.  This means that the curve starts from [tex]-\infty[/tex] to [tex]+\infty[/tex]

Hence, the domain of the function is: [tex](-\infty,\infty)[/tex]

To determine the range, we simply observe the y-axis.

The curve of g(x) starts at y = 3 on the y-axis and the curve faces upward direction.  This means that the curve of g(x) is greater than 3 on the y-axis.

Hence, the range of the function is: [tex](3,\infty)[/tex]

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Function: [tex]g(x) = 3^{x} + 3[/tex]. Domain: [tex]Dom \{g(x)\} = \mathbb{R}[/tex], Range: [tex]Ran \{g(x) \} = (3, +\infty)[/tex], respectively.

In Function Theory, the domain of a function [tex]f(x)[/tex] represents the set of values of the independent variable ([tex]x[/tex]), whereas the range of the function is the set of values of the dependent variable.

The Domain of the Function represents the set of values of [tex]x[/tex] (horizontal axis), whereas the Range it is the set of values of [tex]y[/tex] (vertical axis). After analyzing the existence of Asymptotes, we complement with graphic approaches and conclude where domain and range (in Interval notation) are.

Analytically speaking, the domain of exponential functions is the set of all real numbers and the range of [tex]g(x)[/tex] is any number between [tex]\lim_{x \to -\infty} g(x)[/tex] and [tex]\lim_{x \to +\infty} g(x)[/tex]. In a nutshell, we get the following conclusions in interval notation:

Domain: [tex]Dom \{g(x)\} = (-\infty, +\infty)[/tex], Range: [tex]Ran \{g(x) \} = (3, +\infty)[/tex]

Lastly, we proceed to complement this analysis by graphing function with the help of a graphing tool.

According to the image, domain and range coincides with outcomes from analytical approaches.

find an odd natural numbers x such that LCM (x, 40) = 1400​

Answers

Answer:

175

Step-by-step explanation:

so, the LCM is the combination of the longest chains of the prime factors in every number.

40 : 2, 2, 2, 5

1400 / 40 = 35

35 : 5, 7

but LCM(35, 40) = 2×2×2×5×7 = 280

and not 1400.

what is missing ?

1400 / 280 = 5

aha, another prime factor 5 is missing to get 1400.

x : 5, 5, 7

so, x = 5×5×7 = 175

LCM(175, 40) = 2×2×2×5×5×7 = 1400

Change the following to percentages:
a) 83 out of 100
b) 24 out of 50
c) 9 out of 25
d) 7 out of 20
e) 6 out of 10
f)72 out of 200
g)12 out of 40
h)36 out of 60

Answers

Answer:

a.83%

b. 48%

c.36%

d.35%

e.69%

f.36%

g.30%

h.69%

14. The data below show the average ages and number of volunteer hours for five randomly chosen persons. Given the equation of the regression line is y' = 9.309x - 167.012, predict the number of hours a person will volunteer if her age is 27.5 years. Age, x Volunteer Hours, y 24.9 66.5 25.6 70.0 26.1 74.8 27.3 89.6 27.0 82.6​

Answers

The Predicted time a person will serve is "88.9855 months". A complete solution is provided below.

Given equation is,

→ [tex]\hat{y}=9.309x - 167.012[/tex]

Her age,

→ x = 27.5 years

By substituting the value of "x" in the given equation, we get the predicted time,

hence,

→ [tex]\hat{y}=9.309\times 27.5 - 167.012[/tex]

     [tex]= 255.9975- 167.012[/tex]

     [tex]=88.9855 \ months[/tex]

Thus the above is the right answer

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Which of the following equations is of a parabola with a vertex at (1, 2)?
O y = (x - 1) 2 - 2
Oy= (x - 1)2 + 2
O y = (x + 1)2 - 2
O y = (x + 1)2 + 2

Answers

Answer:

the second option: (x-1)squared +2

Explanation:

The x value of the vertex can be found in the parenthesis after the x. However, you have to do the opposite value of it. So, since the paranthesis has (x-1) then that means that the vertex's x-value has to be 1.

For the y-value of the vertex, that can be found after the paranthesis. This value will not be used as the opposite like with the x-value. So, we know that in (x-1)^2 +2 the "+2" indicates the y-value to be 2.


add 10 and g, then subtract f from the result​

Answers

Answer:

(10+g) -f

Step-by-step explanation:

Add 10 and g

10 +g

Subtract f from the result

(10+g) -f

· f(x)= x2 - 49
Identify the number of zeros of the polynomial function

Answers

Answer:

x = -7, x = 7

Step-by-step explanation:

Firstly, you are going to set the equation to 0, and then factor it.

Set equation to 0 -----> f(x)= x^2 - 49 will become x^2 - 49 = 0

Now, you're going to factor the equation.

You'll get (x-7) (x+7) upon factoring.

Thirdly, you will set (x-7)(x+7) equal to 0 and also solve for x.

Keep in mind that you'll be treating them as two separate equations

So, ----> (x-7) = 0 (x+7) = 0

When you solve for the x, you'll find out that x is equal to 7 and -7 ---> these are your zeros.

question is in picture

Answers

Answer: A

Step-by-step explanation:

(tangent is opposite over adjacent)

[tex]tan(40)=\frac{x}{3.8}\\x=3.8*tan(40)[/tex]

A truck can be rented from Company A for $120 a day plus $0.80 per mile. Company B charges $50 a day plus $0.90 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for Company A and Company B are the same.​

Answers

Answer:

700 miles driven in a day

Step-by-step explanation:

Create an equation to represent the situation, where x is the number of miles.

0.8x + 120 = 0.9x + 50

Solve for x:

120 = 0.1x + 50

70 = 0.1x

700 = x

So, the rental costs will be the same at 700 miles driven in a day.

¿How you solve?

A pool is 8 m long, 6 m wide and 1.5 m deep. It is painted at $6 per square meter.

a) How much will it cost to paint it?
b) How many litres of water will be needed to fill it?

Answers

9514 1404 393

Answer:

  a) $540 cost to paint

  b) 72000 liters to fill

Step-by-step explanation:

Relevant formulas are ...

  P = 2(L +W) . . . . perimeter of a rectangle of length L and width W

  A = LW . . . . . . area of a rectangle of length L and width W

  V = LWH . . . volume of a cuboid of length L, width W, and height H

__

a) The total painted area is the area of the pool walls plus the area of the pool bottom. The wall area is the product of pool perimeter and wall height. The bottom area is the product of pool length and width.

  A = PH + LW = 2(L +W)H +LW

  A = 2(8 m +6 m)(1.5 m) + (8 m)(6 m) = 42 m² +48 m² = 90 m²

At $6 per square meter, the cost of painting the pool is ...

  ($6 /m²)(90 m²) = $540 . . . . cost to paint the pool

__

b) The volume in liters is best figured using the dimensions in decimeters.

  V = (80 dm)(60 dm)(15 dm) = 72000 dm³ = 72000 L

72000 liters will be needed to fill the pool.

-7x-17=2x+10
Show work

Answers

-7x-17=2x+10

2x+7x= -17 -10

9x= - 27

x = – 27/ 9

x= –3

I hope I helped you^_^

The equation cos(35•) = a/25 can be used to find the length of BC what is the length of BC round to the nearest tenth

Answers

Idrk tbh I need help with the same thing

What are the measures of Angles a,b, and c? show your work and explain your answers.​

Answers

Answer:

a=35

b=55

c=110

Step-by-step explanation:

a=35

Opposite angles which are non-adjacent angles formed by two intersecting lines are equal

b+35+90=180 sum of interior angle of a triangle equal to 180

b=180-125

  =55

c+70=180  Angles on a straight line add up to 180°

c=180-70

 =110

How much can 1/2 go into 25

Answers

Answer:

50

Step-by-step explanation:

please mark me as brainliest

Answer:

50

Step-by-step explanation:

Hi there!

Determining how much 1/2 can go into 25 is the same as solving for 25÷1/2:

[tex]25\div\frac{1}{2}[/tex]

Dividing by a fraction is the same as multiplying its reciprocal:

[tex]=25\times\frac{2}{1}\\=25\times2\\=50[/tex]

I hope this helps!

HELP SOMEONE FOR 20 POINTS

Answers

Use the quadratic formula, and it will give you x= 8/3 and 2/5
You can also just use photo math
Using the quadratic formula, your answer will be
X= 2/5 and 8/3

To convert a measurement in centimeters to meters, you simply move the decimal point

Answers

Answer:

there are 100 cm in every meter which means that dividing will convert ot to meters. you can make the conversion quick and easy by simply moving the decimal point in your measurement 2places or place values to left

Step-by-step explanation:

hope it will help you

Need the value of P please

Answers

Answer:

B. 35°

Step-by-step explanation:

First, find the two interior angles that are adjacent to angles 90° and 125° respectively.

Thus:

Interior angle 1: 180° - 90° = 90° (linear pair)

Interior angle 2: 180° - 125° = 55° (linear pair)

P + 90° + 55° = 180° (sum of interior angles in a triangle)

P + 145° = 180°

Subtract 145° from each side

P = 180° - 145°

P = 35°

what is the value of g​

Answers

Answer:

the value of g is gram .

may this answer is helpful for you

Given f (x) = 3x - 5 find f (x - 2)

Answers

Answer:

3x-11

Step-by-step explanation:

f (x) = 3x - 5

f(x-2)

Replace x in the function with x-2

f (x-2) = 3(x-2) - 5

           =3x-6 -5

           =3x-11

A prism and two nets are shown below: Prism 1 E 3 Net A Net Part A: Which is the correct net for the prism? Explain your answer. (2 points) Part B: Write the measurements of Sides AB. BC, and CD of the correct net. (4 points) Part C: What is the surface area of the prism? Show your work. (4 points)​

Answers

Answer:

A) Net A (see explanation)

B) AB = 3 in. | BC = 5 in. | CD = 7.2 in.

C) SA = 98.4 in²

Step-by-step explanation:

Part A

Net A is the correct net for the prism. If you look at the way the folds are, the flaps on the top and bottom would fold up to make the side of the prism. On net B, the flaps wouldn’t fit the shape correctly.

Part B

AB = This is the height of the prism.

= 3 in.

BC = This is the slant on the front of the prism.

= 5 in.

CD = This is the length of the prism.

= 7.2 in.

Part C

* First we’ll solve for the two triangles. They are the same shape and size, so we just need to solve one then duplicate it.

One triangle:

A = 1/2bh

= 1/2 (4) (3)

= 6 in²

Back rectangle:

A = bh

= 7.2 (3)

= 21.6 in²

Front rectangle:

A = bh

= 7.2 (5)

= 36 in²

Bottom rectangle:

A = bh

= 7.2 (4)

= 28.8 in²

Total:

A = 6 + 6 + 21.6 + 36 + 28.8

= 98.4 in²

If y varies inversely with the square of x, and y = 26 when x = 4, find y when x = 2.

A. 13
B. 52
C. 208
D. 104

Answers

Answer:

D. 104

Step-by-step explanation:

[tex]y \: \alpha \: \frac{1}{ {x}^{2} } \\ \\ y = \frac{k}{ {x}^{2} } [/tex]

when y is 26, x is 4:

[tex]26 = \frac{k}{ {(4)}^{2} } \\ k = 416[/tex]

when x is 2:

[tex]y = \frac{416}{ {x}^{2} } \\ \\ y = \frac{416}{ {(2)}^{2} } \\ y = 104[/tex]

Answer:

D; 104

This is the correct answer

A hacker is trying to guess someone's password. The hacker knows (somehow) that the password is 10 characters long, and that each character is either a lowercase letter, (a, b, c, etc.), an uppercase letter (A, B, C, etc.) or a numerical digit (0, 1, 2, 3, 4, 5, 6, 7, 8, or 9). Assume that the hacker makes random guesses.

What is the probability that the hacker guesses the password on his first try? Enter your answer as a decimal or a fraction, not a percentage.​

Answers

The probability that the hacker guesses the password on his first try is:

P = 1/(62^10) = 1.19*10^(-18)

We know that the password is 10 characters long.

In each one of these, we can put.

One lower case letter (26 of these)

One upper case letter (26 of these)

one numerical digit (10 of these)

So, for every single digit, we have a total of:

26 + 26 + 10 = 62 options

Now we can find the total number of different passwords, which will be equal to the product between the number of options for each one of the characters.

We know that for each character we have 62 different options.

And we have 10 characters.

Then the product between the numbers of options is:

C = 62^10

Then if the hacker does a random guess, the probability that the random guess is correct is one over the total number of possible combinations.

P = 1/C = 1/(62^10)

The probability that the hacker guesses the password on his first try is:

P = 1/(62^10) = 1.19*10^(-18)

If you want to read more about probability, you can read:

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Choose the slope-intercept form of 3x + 2y = 5.
3.
у==x
5
2.
O
O y=-x+
5
0
5
v=-x+
O
yox
5
3

Answers

Answer:

y = -3x/2 + 5/2

Step-by-step explanation:

Well, basically what you do is modify it so that y is on one side.

3x+2y = 5

2y = 5-3x

y = (5-3x)/2

y = 5/2 -3x/2

So, the answer is the second option.

Answer:

B

Step-by-step explanation:

3x + 2y = 5

Our goal is this form:

y = mx + b

- move 3x to right anc change its sign

2y = -3x + 5

- divide each member by 2

y = -3/2 x + 5/2



Mini wants to buy a scooter for Rs 62,000 . She has only Rs 19,000 with her, so she decides to take a loan from a bank for the remaining amount. The bank offers Mini three loan schemes as shown below. Mini has to return the loan amount with interest in equal monthly instalments

2) Which among the given schemes offers a monthly instalment of less than Rs 5000. ?

a) Scheme A
b) Scheme B
c) Scheme C
d) Both Scheme A and Scheme B​

Answers

I think scheme c Rs48,000 is the answer

An education researcher would like to test whether 2nd graders retain or lose knowledge during the summer when they are presumably not in school. She asks nine 2nd graders to take a comprehension exam at the end of the school year (May), and then asks those same students to come back after the summer (late August) to retake a different but equivalent exam, to see if their level of comprehension has changed. Using the data below, test this hypothesis using an (alpha level of 0.05.)

May August
95 100
72 80
78 95
50 65
89 85
92 98
75 70
90 96
65 87

Required:
What is the appropirate test?

Answers

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data:

May August

95 100

72 80

78 95

50 65

89 85

92 98

75 70

90 96

65 87

The appropriate test is a paired t test :

d = difference between May and August

d = (-5, -8, -17, -15, 4, -6, 5, -6, -22)

The hypothesis :

H0 : μd = 0

H1 : μd ≠ 0

The test statistic :

T = dbar / (Sdbar/√n)

Where, dbar and Sdbar are the mean and standard deviation of 'd' respectively.

Using calculator :

dbar = - 7.777 ; Sdbar = 9.052

Test statistic = - 7.777 / (9.052 /√9)

Test statistic = - 2.577

The Pvalue, df = n - 1 = 9 - 1 = 8

Pvalue(-2.577, 8) = 0.0327

At α = 0.05

Pvalue < α ; WE reject the H0 ; and conclude that there has been a change in score

Solve the inequality is it a,b,c,d?

Answers

Answer:

B

Step-by-step explanation:

-2/3x<31/3

x>-31/2

x>-15 1/2

Answer:

x > - 15 1/2

Step-by-step explanation:

-2/3 x -10 < 1/3

Multiply each side by 3

3(-2/3 x -10 < 1/3)

-2x -30 < 1

Add 30 to each side

-2x-30+30 <1+30

-2x < 31

Divide by -2 remembering to flip the inequality

-2x/-2 > 31/-2

x > -31/2

x > - 15 1/2

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