A bottle maker believes that 23% of his bottles are defective. If the bottle maker is accurate, what is the probability that the proportion of defective bottles in a sample of 602 bottles would differ from the population proportion by less than 4%

Answers

Answer 1

Answer:

0.9802 = 98.02% probability that the proportion of defective bottles in a sample of 602 bottles would differ from the population proportion by less than 4%

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

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.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

A bottle maker believes that 23% of his bottles are defective.

This means that [tex]p = 0.23[/tex]

Sample of 602 bottles

This means that [tex]n = 602[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.23[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.23*0.77}{602}} = 0.0172[/tex]

What is the probability that the proportion of defective bottles in a sample of 602 bottles would differ from the population proportion by less than 4%?

p-value of Z when X = 0.23 + 0.04 = 0.27 subtracted by the p-value of Z when X = 0.23 - 0.04 = 0.19.

X = 0.27

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

By the Central Limit Theorem

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

[tex]Z = \frac{0.27 - 0.23}{0.0172}[/tex]

[tex]Z = 2.33[/tex]

[tex]Z = 2.33[/tex] has a p-value of 0.9901

X = 0.19

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

[tex]Z = \frac{0.19 - 0.23}{0.0172}[/tex]

[tex]Z = -2.33[/tex]

[tex]Z = -2.33[/tex] has a p-value of 0.0099

0.9901 - 0.0099 = 0.9802

0.9802 = 98.02% probability that the proportion of defective bottles in a sample of 602 bottles would differ from the population proportion by less than 4%


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(-1;2;-3)

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Answers

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Step-by-step explanation:

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Answer

900

Step-by-step explanation:

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5 x 18 x 10 = 900cm³

Water is flowing into a tank at a rate of 20 cm3/min. At the start, there is 250 cm3 of water in the tank.
(i) How much water will be in the tank after 30 minutes?
(ii) Find the time when there is 1210 cm3 of water in the tank.

Answers

Answer:

i) 410 cm³

ii) 48 min

Step-by-step explanation:

we start with 250 cm³.

and then we fill in 20 cm³ per minute.

i)

after 30 minutes we have

250 + 8×20 = 250 + 160 = 410 cm³

ii)

how long (how many minutes) does it take to reach 1210 cm³ in the tank ?

well, first we subtract the start amount (250).

and then we see how often 20 cm³ will "fit" into the remainder. and then we know how many minutes the water has to run.

1210 - 250 = 960 cm³

so, the incoming water needs to reach 960 cm³ to have a total of 1210 cm³.

and

960 cm³ / (20 cm³ / min) = 960 cm³ min / 20 cm³ =

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Answers

Answer:

u = 18

Step-by-step explanation:

The two angles 3u and u+36 are equal so

3u = u+36

Subtract u from each side

3u -u = u+36-u

2u = 38

Divide by 2

2u/2 = 36/2

u = 18

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Answers

Answer:

5/2 or 2½ or 2.5

Step-by-step explanation:

20/8 = 2.5

10/4 = 2.5

Assume that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true standard deviation 0.74. (a) Compute a 95% CI for the true average porosity of a certain seam if the average porosity for 19 specimens from the seam was 4.85. (Round your answers to

Answers

Answer:

The answer is "(4.518, 5.182)"

Step-by-step explanation:

[tex]\sigma = 0.74[/tex]

The aveage porosity for a sample of [tex]n = 19[/tex] specimens is

[tex]\bar{x}=4.85[/tex]

Thus, the[tex]95\%[/tex] confidence interval for the true mean is

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Therefore, one can state that the true average porosity will lie  between 4.518 and 5.182 with the 95\% confidence.

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Answers

Answer:

50,000

Step-by-step explanation:

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I hope this helps!

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Answers

Answer:

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Answer:

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Step-by-step explanation:

another way of doing this type of calculation is...

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Answers

Line is the answer ,,,,

Answer:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answer:

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Answers

Answer:

Adam runs at a rate of 11 minutes per mile.

Step-by-step explanation:

Take 143 minutes and divide by 13 miles and you will get the answer of 11 minutes.

PLEASE MARK ME BRAINEIST.

Answer:

it would take him 11 minuets to run a mile

Step-by-step

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Answers

Answer: hello your question is poorly written attached below is the complete question

answer:

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attached below is the solution

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Answers

Answer:

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Answers

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Step-by-step explanation:

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It’s 4(4x-4)
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Answers

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Step-by-step explanation:

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  A: 0.0625

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__

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7. Solve for x: x/6 - y/3 = 1

Please give steps! ❤️

Answers

[tex]\\ \sf\longmapsto \frac{x}{6} - \frac{y}{3} = 1 \\ \\ \sf\longmapsto \frac{x - 2y}{6} = 1 \\ \\ \sf\longmapsto x - 2y = 6 \\ \\ \sf\longmapsto x = 6 + 2y[/tex]

One time Maria took 27 minutes to walk 1.8km to school. She left home at 07:48 . Write down the time Maria arrived at school

Answers

Answer:

8:15

Step-by-step explanation:

the time would be 8:15 7:48 + 27 = 8:15

I need helpppp please I don’t understand this question at alll

Answers

Answer:

17000

Step-by-step explanation:

17^1 * 10^3

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17*1000

17000

the answer is 17,000

the exponent shows how many times you multiply the number by itself

here is an image for an explanation

hope I helped ❤

two cars started to move towards each other at the same time. the speed of the first car was twice the speed of the second car. they met in two hours. if the distance traveled altogether was 300 km find the rates of the cars.

Answers

Answer:

Step-by-step explanation:

Let v be the speed of the slower car

2v is the speed of the faster car

In 2 hrs, the slower car travels a distance of

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Answers

Answer:

7 quarts

Step-by-step explanation:

total paint = paint used + paint left

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Answers

Answer:

(x + 4)² + (y + 10)² = 9

Step-by-step explanation:

The standard equation of a circle is written as seen below

(x - h)² + (y - k)² = r²

Where (h,k) is at the center and r is the radius

We want to find the standard equation of a circle that has a radius of 3 and a center at (-4,-10)

Remember r = radius so r = 3

and (h,k) is at center so h = -4 and k = -10

Now to find the standard equation of the circle we simply plug in the values of the variables (h,k and r) into the standard equation of a circle formula.

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(x - (-4))² + (y - (-10))² = 3²

Simplify

(x + 4)² + (y + 10)² = 9

And we are done!

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Answer:

Mark me brainlist please please please please

Answer:

Step-by-step explanation:

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I drew it so here’s an example

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Vẽ góc vuông. - Trên hai canh góc vuô dùng thước thước có chia khoảng vẽ hai đoạn thẳng bằng nhau có chung một điểm và nối hai điểm còn lại.

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