How do you round up to the nearest hundreth

Scatter plot shows negative correlation; regression equation: Defective Parts = [tex]27.5 - 0.3 \times \text{Line Speed}[/tex]; 20 defects predicted at 25 fpm.

a. The scatter diagram with the line speed as the independent variable is displayed. It shows the number of defective parts found at various line speeds.

(DIAGRAM IS GIVEN BELOW)

b. The scatter diagram indicates that there is a negative relationship between the two variables. As the line speed increases, the number of defective parts found decreases. This suggests that at higher speeds, perhaps the inspectors are not able to identify all the defective parts due to the speed at which the parts are moving past the inspection station.

c. Using the least squares method to develop the estimated regression equation with line speed as the independent variable (to 1 decimal), we get:

Defective Parts = [tex]27.5 - 0.3 \times \text{Line Speed}[/tex]

where 27.5 is the y-intercept and -0.3 is the slope of the line.

d. To predict the number of defective parts found for a line speed of 25 feet per minute, we can substitute x = 25 into the regression equation:

Defective Parts = [tex]27.5 - 0.3 \times 25 = 20.0[/tex]

Therefore, the model predicts that for a line speed of 25 feet per minute, there would be 20 defective parts found.

The complete question is here:

Brawdy Plastics, Inc. produces plastic seat belt retainers for General Motors at their plant in Buffalo, New York. After final assembly and painting, the parts are placed on a conveyor belt that moves the parts past a final inspection station. How fast the parts move past the final inspection station depends upon the line speed of the conveyor belt (feet per minute). Although faster line speeds are desirable, management is concerned that increasing the line speed too much may not provide enough time for inspectors to identify which parts are actually defective. To test this theory, Brawdy Plastics conducted an experiment in which the same batch of parts, with a known number of defective parts, was inspected using a variety of line speeds. The following data were collected. If required, enter negative values as negative numbers.

(DATA IS GIVEN BELOW)

a. Select a scatter diagram with the line speed as the independent variable.

b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?

c. Use the least squares method to develop the estimated regression equation (to 1 decimal). = + x d. Predict the number of defective parts found for a line speed of 25 feet per minute.

1 meter = 1,000 millimeter

We can solve this by making two proportion or millimeter over meter:  [tex]\frac{millimeter}{meter}[/tex]

[tex]\frac{19.5 mm}{x meter} = \frac{1,000 mm}{1 m}[/tex]

Now you must solve for the unknown meter under the first proportion:

(1,000)(x meter) = 19.5 * 1

1,000(x meter) = 19.5

x meter = 0.0195 m

19.5 mm = 0.0195 m

Hope this helped! Let me know if you have any further questions

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Answer:

[tex]t=\frac{424-420}{\frac{26}{\sqrt{61}}}=1.202[/tex]    

[tex]p_v =2*P(t_{(60)}>1.202)=0.234[/tex]  

If we compare the p value and the significance level given [tex]\alpha=0.01[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can conclude that the true mean is NOT different from  420. So the specification is satisfied.

Step-by-step explanation:

Data given and notation  

[tex]\bar X=424[/tex] represent the sample mean

[tex]s=26[/tex] represent the sample standard deviation

[tex]n=61[/tex] sample size  

[tex]\mu_o =420[/tex] represent the value that we want to test

[tex]\alpha=0.01[/tex] represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the true mean is different from 420 or not, the system of hypothesis would be:  

Null hypothesis:[tex]\mu = 420[/tex]  

Alternative hypothesis:[tex]\mu \neq 420[/tex]  

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic

We can replace in formula (1) the info given like this:  

[tex]t=\frac{424-420}{\frac{26}{\sqrt{61}}}=1.202[/tex]    

P-value

The first step is calculate the degrees of freedom, on this case:  

[tex]df=n-1=61-1=60[/tex]  

Since is a two sided test the p value would be:  

[tex]p_v =2*P(t_{(60)}>1.202)=0.234[/tex]  

Conclusion  

If we compare the p value and the significance level given [tex]\alpha=0.01[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can conclude that the true mean is NOT different from  420. So the specification is satisfied.

The question involves calculating compound interest using a given principal, interest rate, and time period. The calculation is performed using the compound interest formula, which takes into account the principal amount of $1000, an annual interest rate of 4.8%, and a time span of 2 years.

The question pertains to calculating compound interest over a certain period using a principal amount, an annual interest rate, and a given time frame. Given a principal of $1000, an annual interest rate of 4.8%, and a time period of 2 years, we can find the amount of interest accrued using the formula:

Interest = Principal  imes rate  imes time

Compound Interest = Principal  imes (1 + interest rate)time

In this case, the formula would be:

Compound Interest = $1000  imes (1 + 0.048)2

Performing this calculation would give us the total amount after 2 years, including both the principal and the interest earned.

Answer:

2345

Step-by-step explanation:

because3456

Answer:

A ^2 + B^2 =C^2. The Pythagorean Theorem is a statement about triangles containing a right angle

Step-by-step explanation:

Given:

The given two functions are [tex]f(x)=\frac{4 x^{2}+24 x}{x^{2}-11 x+30}[/tex]  and  [tex]g(x)=\frac{x-5}{x^{2}}[/tex]

We need to determine the value of R(x)

Value of R(x):

The value of R(x) can be determined by R(x) = f(x) × g(x)

Substituting the values, we get;

[tex]R(x)=\frac{4 x^{2}+24 x}{x^{2}-11 x+30} \cdot \frac{x-5}{x^{2}}[/tex]

Multiplying the fractions, we have;

[tex]R(x)=\frac{\left(4 x^{2}+24 x\right)(x-5)}{\left(x^{2}-11 x+30\right) x^{2}}[/tex]

Let us factor out the common term 4x from the term (4x² + 24x)

Thus, we have;

[tex]R(x)=\frac{4 x(x+6)(x-5)}{\left(x^{2}-11 x+30\right) x^{2}}[/tex]

Let us factor the term (x² -11x + 30), we get;

[tex]R(x)=\frac{4(x+6)(x-5)}{x(x-5)(x-6)}[/tex]

Cancelling the common term, we have;

[tex]R(x)=\frac{4(x+6)}{x(x-6)}[/tex]

Thus, the value of R(x) is [tex]\frac{4(x+6)}{x(x-6)}[/tex]

Answer: The expected frequency for the Business college is 31.5.

Step-by-step explanation:

Since we have given that

Number of students from ABC university = 300

Number of students from Liberal Arts college = 120

Number of students in Education college = 90

Number of students in Business college = 90

Probability of students in Business college = 35% = 0.35

Probability of students in Liberal arts college = 0.35

Probability of students in Education college = 0.30

So, Expected frequency for the Business College is given by

[tex]0.35\times 90=31.5[/tex]

Hence, the expected frequency for the Business college is 31.5.

Answer: the answer is zero my bad

Step-by-step explanation:

Answer:

The length of the rectangle is

12

c

m

and the area of the rectangle is

60

c

m

2

.

Explanation:

By definition, the angles of a rectangle are right. Therefore, drawing a diagonal creates two congruent right triangles. The diagonal of the rectangle is the hypotenuse of the right triangle. The sides of the rectangle are the legs of the right triangle. We can use the Pythagorean Theorem to find the unknown side of the right triangle, which is also the unknown length of the rectangle.

Recall that the Pythagorean Theorem states that the sun of the squares of the legs of a right triangle is equal to the square of the hypotenuse.

a

2

+

b

2

=

c

2

5

2

+

b

2

=

13

2

25

+

b

2

=

169

25

−

25

+

b

2

=

169

−

25

b

2

=

144

√

b

2

=

√

144

b

=

±

12

Since the length of the side is a measured distance, the negative root is not a reasonable result. So the length of the rectangle is

12

cm.

The area of a rectangle is given by multiplying the width by the length.

A

=

(

5

c

m

)

(

12

c

m

)

A

=

60

c

m

2

Answer:

[tex] {5}^{2} + {x}^{2} = {13}^{2} \\ 25 + {x}^{2} = 169 \\ {x}^{2} = 169 - 25 \\ {x}^{2} = 144 \\ x = \sqrt{144} \\ x = 12cm[/tex]

Step-by-step explanation:

use the Pythagorean theorem

hope this helps you

Answer:

a) The null hypothesis is represented as

H₀: μ ≤ 23

The alternative hypothesis is given as

Hₐ: μ > 23

b) Check the Explanation

The conditions for a t-test to be performed are satisfied or not?

- Yes, because the students were randomly sampled.

- Yes, the sample size is larger man 30.

And the central limit theorem allows us to approximate that the random sample obtained from the population is a normal distribution.

c) Are the sampled values independent of each other?

Yes, because each student's test score does not affect other students' test scores.

d) p-value obtained = 0.004

Reject the null hypothesis because the P-value a less than the alpha = 0.10 level of significance

e) There is sufficient evidence to conclude that the population mean is greater than 23.

Step-by-step explanation:

For hypothesis testing, the first thing to define is the null and alternative hypothesis.

The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.

While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.

For this question, we want to check if results suggest that students who complete the core curriculum are ready for college-level mathematics.

The only condition to be ready for college is scoring above 23.

So, the null hypothesis would be that the mean of test scores of students that complete core curriculum is less than or equal to 23. That is, there isn't significant evidence to conclude that the results suggest that students who complete the core curriculum are ready for college-level mathematics.

And the alternative hypothesis would be that there is significant evidence to conclude that the results suggest that students who complete the core curriculum are ready for college-level mathematics. That is, the mean score of those that complete the core curriculum is above 23 and are ready for college-level mathematics.

Mathematically

The null hypothesis is represented as

H₀: μ ≤ 23

The alternative hypothesis is given as

Hₐ: μ > 23

b) The conditions required before performing t-test.

- The sample should be a random sample

- The dependent variable should be approximately normally distributed.

- The observations are independent of one another.

- The dependent variable should not contain any outliers

All of these conditions are satisfied for our distribution.

c) Are the sampled values independent of each other?

Yes, because each student's test score does not affect other students' test scores.

d) To do this test, we will use the t-distribution because no information on the population standard deviation is known

So, we compute the t-test statistic

t = (x - μ₀)/σₓ

x = sample mean = 23.6

μ₀ = 23

σₓ = standard error = (σ/√n)

where n = Sample size = 200

σ = Sample standard deviation = 3.2

σₓ = (3.2/√200) = 0.226

t = (23.6 - 23) ÷ 0.226 = 2.65

checking the tables for the p-value of this t-statistic

- Degree of freedom = df = n - 1 = 200 - 1 = 199

- Significance level = 0.10

- The hypothesis test uses a one-tailed condition because we're testing only in one direction.

p-value (for t = 2.65, at 0.10 significance level, df = 199, with a one tailed condition) = 0.004348 = 0.004 to 3 d.p.

The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 0.10

p-value = 0.004

0.004 < 0.10

Hence,

p-value < significance level

This means that we reject the null hypothesis, accept the alternative hypothesis and say that there is significant evidence to conclude that the results suggest that students who complete the core curriculum are ready for college-level mathematics. That is, the mean score of those that complete the core curriculum is above 23 and are ready for college-level mathematics.

e) The result of the p-value obtained is that there is significant evidence to conclude that the results suggest that students who complete the core curriculum are ready for college-level mathematics. That is, the mean score of those that complete the core curriculum is above 23 and are ready for college-level mathematics.

Hope this Helps!!!

Answer:

4 * x - 33

Step-by-step explanation:

four times as old as she was 33 years ago

let x represent how old she is now

4 * x - 33

Four ( 4 ) times ( * ) as old as she was 33 years ago ( x - 33 )

Final answer:

The phrase "4 times as old as she was 33 years ago" can be represented algebraically as the equation x = 4(x - 33), where x is the current age of the person.

Explanation:

To translate the phrase "4 times as old as she was 33 years ago" into algebraic terms, we first denote the current age of the person as a variable, let's call it x. The age of the person 33 years ago would then be expressed as x - 33. To articulate that someone is now four times as old as they were 33 years ago, we create the algebraic expression 4(x - 33), which represents the current age being four times the age 33 years prior.

Example:

If we want to set up an equation where someone's current age is four times their age from 33 years ago, it would look like this:

Let x = current age

Then x - 33 = age 33 years ago

The phrase translates to the equation x = 4(x - 33)

By multiplying both sides by the same factor, we can manipulate this equation if necessary to solve for x. As an example, multiplying both sides by 1 does not change the equation, but it can sometimes be helpful in other contexts to multiply both sides to simplify or to get rid of fractions.

Answer:

See the image below.

The lower of cost or market rule states that a business must record the cost of inventory at whichever cost is lower – the original cost or its current market price.

To determine the carrying value of inventory under the lower of cost or market (LCM) rule, we compare unit cost and unit replacement cost for each product and choose the lower value. We then multiply these values with their respective quantities and sum them to get the total carrying value. For inventory write-downs, we record an adjustment entry.

The carrying value of inventory for Forester Company at the end of December 31, 2018, involves two scenarios. In the first scenario, we apply the lower of cost or market (LCM) rule to individual products (product A through E). For each product, we compare its unit cost and unit replacement cost and choose the lower value. The total carrying value under this scenario is obtained by summing the products of the chosen values and the respective quantities.

In the second scenario, we apply the LCM rule to the entire inventory. Here, we compare the total cost and the total replacement cost of all products, and choose the lesser value as the carrying value of inventory. Inventory write-downs are typical business practice for Forester, in this case, we record an adjusting entry to recognize the loss resulting from decline in the value of inventory.

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Answer:

70 degrees.

Step-by-step explanation:

Hello!

It says that this triangle is a right triangle. That means one angle is 90°. Since there are 180° in a triangle, all we have to do is subtract 90 + 20 from 180.

90 + 20 = 110

180 - 110 = 70.

So the medium angle is 70°.

Hope this helps!

Answer:

Your answer is B

Step-by-step explanation:

i just did the test

Answer:$7.50

Step-by-step explanation:

Answer:

523.333333333

Step-by-step explanation:

Using the formula 4/3πr³:

(4/3)(3.14)(5^3)

Hope this helps :)

Answer:

h = 5

Step-by-step explanation:

[tex] \frac{h}{6} = \frac{20}{24} \\ 24 \times h = 20 \times 6 \\ 24h = 120 \\ h = \frac{120}{24} \\ h = 5[/tex]

Answer:

218

Step-by-step explanation:

327*2/3=218

las otras dos hijas obtendrán 3750 pesos y 2000 pesos.

Cuando dos números son divisibles se pueden escribir en la forma p:q, cuando dos razones son iguales se dice que son proporcionales.

El padre da dinero a las hijas en la proporción de su edad.

La hija mayor, que tiene 20 años, da 5.000 pesos.

La relación es 5000: 20 = 250:1

la edad de las otras hijas es 15 y 8

Que la hija de 15 años se lleve x pesos

y la hija de 8 años recibe y pesos

por lo que se forma la relación x: 15 y x: 8 que es igual a 250: 1

Comparando las dos proporciones

x/15 = 250/1

X = 15*250

x = 3750 pesos

x/8 = 250/1

x = 2000 pesos

Por lo tanto, las otras dos hijas obtendrán 3750 pesos y 2000 pesos.

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Answer:

top 83 1/5

bottom 1,248

Step-by-step explanation:

i got it right

Answer:

Top 83 1/5

Bottom 1,248

Step-by-step explanation:

Just took it

Answer:

a) 50.41% probability that neither will need repair.

b) 8.41% probability that both will need repair.

c) 49.59% probability that at least one car will need repair.

Step-by-step explanation:

For each car, there are only two possible outcomes. Either it will need repairs, or it will not need repairs. The probability of a car needing repairs is independent of other cars. So 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.

17​% of cars will need to be repaired​ once, 10​% will need repairs​ twice, and 2​% will require three or more repairs.

This means that [tex]p = 0.17+0.1+0.02 = 0.29[/tex]

Two cars:

This means that [tex]n = 2[/tex]

a) neither will need​ repair?

This is P(X = 0).

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

[tex]P(X = 0) = C_{2,0}.(0.29)^{0}.(0.71)^{2} = 0.5041[/tex]

50.41% probability that neither will need repair.

​b) both will need​ repair? ​

This is P(X = 2).

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

[tex]P(X = 2) = C_{2,2}.(0.29)^{2}.(0.71)^{0} = 0.0841[/tex]

8.41% probability that both will need repair.

c) at least one car will need​ repair?

Either none will need repair, or at least one will. The sum of these probabilities is 100%.

From a)

50.41% probability that neither will need repair.

p = 100 - 50.41 = 49.59%

49.59% probability that at least one car will need repair.

Answer:(x,y) = (-2,2)

Step-by-step explanation:

Answer:

Копиравать

Step-by-step explanation:

Копиравать ладно

Based on the information given, it should be noted that the Wilcoxon signed rank test will be 3.

From the table, it can be seen that the first tank is assigned to the first absolute value. The second rank is assigned to the second absolute value while the average of the third and the fourth value are given the value of 3.

The sum of the positive ranks will be:
= 1 + 2 = 3

The sum of the negative ranks will be:
= 8 + 7 + 3.5 + 3.5 + 6 + 5 = 33.

Therefore, the Wilcoxon signed-rank will be the minimum of 33 and 3 which is 3.

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Answer:

  x = y = 26 cm; z = 13 cm

Step-by-step explanation:

The generic solution for the minimum material in an open-top box is that the box is square and half as high as it is wide. It is half a cube of twice the volume.

The dimensions of the square base are ...

  ∛(2·8788 cm³) = 26 cm

Then the height is half that, or 13 cm.

  x = y = 26 cm; z = 13 cm

_____

If you need to see the development, you can use the method of Lagrange multipliers to find the minimum area for the given volume;

  area = xy +2(xz +yz)

  volume = xyz = 8788

We require each of the partial derivatives of L with respect to x, y, z, and λ to be zero.

  L = xy +2(xz +yz) +λ(xyz -8788)

  partial with respect to x: 0 = y+2z +λyz

  partial with respect to y: 0 = x +2z +λxz

  partial with respect to z: 0 = 2x+2y +λxy

  partial with respect to λ: 0 = xyz -8788

From the first two equations, we have ...

  λ = (y +2z)/(yz) = 1/z +2/y

  λ = (x +2z)/(xz) = 1/z +2/x

Equating these expressions for λ, we find ...

  1/z +2/y = 1/z +2/x   ⇒   x = y

The third equation then tells us ...

  λ = (2x +2y)/(xy) = 2/y +2/x

Comparing this to either of the first two expressions for λ, we see ...

  1/z +2y = 2/x +2/y   ⇒   z = x/2

This is the result we started the answer with:

  x = y = 2z = ∛(2·8788 cm³)

Answer:

a and c

Step-by-step explanation:

Looking at the pieces of information, the pieces of information that can be gathered from these box plots are:

Olympics actually refers to the major international event which usually features different sports and normally holds once in every four years. It is also known as the Games of the Olympiad.

From the pieces of information given, we can actually conclude that the above options can be gathered from the information.

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Answer: B

Step-by-step explanation: I believe it's B because if you're able to get the opinions of others about your store. You'll be able to see whats the customers are more interested in, so therefore be able to supply your store with stuff people are more intrigued in. (Let me know if I'm wrong, have a good day)

Answer:

see explanation

Step-by-step explanation:

Given that M is directly proportional to r³ then the equation relating them is

M = kr³  ← k is the constant of proportion

To find k use the condition when r = 4, M = 160, thus

160 = k × 4³ = 64k ( divide both sides by 64 )

2.5 = k

M = 2.5r³ ← equation of variation

(a)

When r = 2, then

M = 2.5 × 2³ = 2.5 × 8 = 20

(b)

When M = 540, then

540 = 2.5r³ ( divide both sides by 2.5 )_

216 = r³ ( take the cube root of both sides )

r = [tex]\sqrt[3]{216}[/tex] = 6

The task involves summarizing previous answers and reflecting upon them using a paragraph planner to organize and provide clarity to the response. This process aids in addressing the questions effectively and personally.

To approach the task at hand, one must begin by summarizing the answers provided previously. It is essential to distill the content into a coherent summary that accurately represents the experiences and advice shared. Upon doing so, reflection on these insights will lead to a personal understanding that is both informed and enriched by the various perspectives.

An effective strategy for this analysis is to use a paragraph planner. This tool assists in organizing thoughts and structuring the response in a logical and clear manner. By leveraging such a planner, the responses to the posed questions will not only address the directly asked matters but also encapsulate a broader interpretation of the information received.

Tonight's endeavor is to answer critical questions that resonate with the audience's collective curiosity. This act of addressing inquiries serves as a bridge between the speaker and the listener, fostering a shared understanding and grounding the conversation in mutual interests and concerns.

Answer:

What is the probability that a randomly selected string with exactly ten characters results in a valid password?  = 0.02836

Step-by-step explanation:

CHECK THE ATTACHMENT BELOOW

Final answer:

The probability of a randomly selected string with exactly ten characters resulting in a valid password can be determined using combinatorics. The probability is given by (62! / (52!*10!)) / (62^10)

Explanation:

To find the probability of a randomly selected string with exactly ten characters resulting in a valid password, we need to determine how many valid passwords exist out of all possible strings of length ten. Since the password must contain at least one character from each of the three sets (upper-case letters, lower-case letters, and digits), we can calculate the probability using combinatorics.

There are 26 upper-case letters, 26 lower-case letters, and 10 digits, so the total number of characters in the union of the three sets is 26 + 26 + 10 = 62.

The probability of selecting a valid password is then:

P(valid password) = (Number of valid passwords) / (Total number of passwords)

For a valid password, the first character can be any of the 62 characters, the second character can be any of the remaining 61 characters, and so on. Therefore, the number of valid passwords is: 62 * 61 * 60 * ... * 53.

Since there are 10 characters in a valid password, the number of valid passwords is:

62 * 61 * 60 * ... * 53 = 62! / (52!*10!).

The total number of passwords of length 10 is: 62^10.

Therefore, the probability of a randomly selected string with exactly ten characters resulting in a valid password is:

P(valid password) = (62! / (52!*10!)) / (62^10).

Answer:

(a) The confidence level desired by the researchers is 95%.

(b) The sampling error is 0.001 microcurie per millilitre.

(c) The sample size necessary to obtain the desired estimate is 36.

Step-by-step explanation:

The mean and standard deviation of the amount of the radioactive​ element, cesium-137 present in a sample of n = 16 lichen specimen are:

[tex]\bar x=0.009\\s=0.003[/tex]

Now it is provided that the researchers want to increase the sample size in order to estimate the mean μ to within 0.001 microcurie per millilitre of its true​ value, using a​ 95% confidence interval.

The (1 - α)% confidence interval for population mean (μ) is:

[tex]CI=\bar x \pm z_{\alpha/2}\times \frac{s}{\sqrt{n}}[/tex]

(a)

The confidence level is the probability that a particular value of the parameter under study falls within a specific interval of values.

In this case the researches wants to estimate the mean using the 95% confidence interval.

Thus, the confidence level desired by the researchers is 95%.

(b)

In case of statistical analysis, during the computation of a certain statistic, to estimate the value of the parameter under study, certain error occurs which are known as the sampling error.

In case of the estimate of parameter using a confidence interval the sampling error is known as the margin of error.

In this case the margin of error is 0.001 microcurie per millilitre.

(c)

The margin of error is computed using the formula:

[tex]MOE=z_{\alpha/2}\times \frac{s}{\sqrt{n}}[/tex]

The critical value of z for 95% confidence level is:

[tex]z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96[/tex]

*Use a z-table.

Compute the sample size value as follows:

[tex]MOE=z_{\alpha/2}\times \frac{s}{\sqrt{n}}[/tex]

      [tex]n=[\frac{z_{\alpha/2}\times s}{MOE}]^{2}[/tex]

          [tex]=[\frac{1.96\times 0.003}{0.001}]^{2}[/tex]

          [tex]=34.5744\\\approx36[/tex]

Thus, the sample size necessary to obtain the desired estimate is 36.

The sample size necessary to estimate the mean within the desired sampling error can be calculated using the formula: n = (z * σ / E)^2, where n is the sample size, z is the z-score corresponding to the desired confidence level, σ is the standard deviation, and E is the desired sampling error. In this case, the sample size is approximately 11,447.

To determine the sample size necessary to estimate the mean within the desired sampling error, we can use the formula:

n = (z * σ / E)^2

Where n is the sample size, z is the z-score corresponding to the desired confidence level (in this case, 1.96 for a 95% confidence level), σ is the standard deviation, and E is the desired sampling error.

Plugging in the values, we get:

n = (1.96 * 0.003 / 0.001)^2

Simplifying, we find that n is approximately 11,447. Therefore, the sample size necessary to obtain the desired estimate is 11,447 (rounded to the nearest whole number).

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