Suppose each laptop of a certain type is assigned a series number, which consists of a sequenceof eight symbols: number, letter, letter, letter, number, number, number, number, where aletter is any one of 26 letters and a number is one among 0, 1,. . ., 9. Assume that all series numbers are equally likely.
(a) What is the probability that all symbols are different if one laptop is picked at random with equal probability?
(b) What is the probability that all symbols are different and the first number is the largest among the numbers?

Volume = length x width x height

120 = 15 x 4 x length

Simplify:

120 = 60 x length

Divide both sides by 60:

Length = 2 feet

Formula for the volume of a rectangular prism: V = length x width x height

120 = l x 4 x 15

120 = l x 60

l = 2

The length of the rectangular prism is 2 feet.

Hope this helps!! :)

Answer:

BURRITOS

Step-by-step explanation:

Answer:

9.66666666 yards  repeating

Step-by-step explanation:

The formula is to divide feet by 3,so 29/3=9.666666 repeating.

Mark me brainliest if I helped:D

Answer:

n=2/3, -1/4

Step-by-step explanation:

Answer:

a) X = N(1955,556)

b) 1955 is the population mean

c) P(X <1911) = 0.4685

d) P(1868 < X <2105) = 0.1685

e) 95th percentile = 2870 (nearest whole number)

Step-by-step explanation:

a) Average number of votes per district, μ = 1955

The standard deviation, [tex]\sigma = 556[/tex]

The distribution of X will take the form [tex]N(\mu, \sigma)[/tex]

Therefore the distribution of X is N(1955,556)

b)1955 is the average of all the votes president Clinton had per district(i.e. the mean of all the values of the population) and not the mean of collected samples.

1955 is the population mean

c) Probability that a randomly selected district had fewer than 1911 votes for president Clinton

[tex]P(X < 1911) = P ( z < \frac{x - \mu}{\sigma} )[/tex]

z=(1911-1955)/556

z=-0.079

From the probability distribution table

P(z<-0.079)=0.4685

Therefore, P(X <1911) = 0.4685

d)probability that a randomly selected district had between 1868 and 2105 votes for President Clinton

[tex]P(x_{1} < X <x_{2}) = P(z_{2} < \frac{x_{2} - \mu }{\sigma} )- P(z_{1} < \frac{x_{1} - \mu }{\sigma} )[/tex]

[tex]P(1868 < X <2105) = P(z_{2} < \frac{2105 - 1955 }{556} )- P(z_{1} < \frac{1868 - 1955 }{556} )\\P(1868 < X <2105) = P(z_{2} < 0.27)- P(z_{1} < -0.16 )[/tex]

P(1868 < X <2105) = 0.6063 - 0.4378

P(1868 < X <2105) = 0.1685

e)  Find the 95th percentile for votes for President Clinton

[tex]P_{95} = \mu + 1.645 \sigma\\P_{95} = 1955 + 1.645(556)\\P_{95} = 2869.62\\P_{95} = 2970[/tex]

P95=1955+1.645*556=2870

The distribution of X is a normal distribution with a sample mean of 1,956.8. The probability of a randomly selected district having fewer than 1,600 votes is approximately 0.267. The probability of a randomly selected district having between 1,800 and 2,000 votes is approximately 0.161. The 95th percentile for votes is approximately 2,885.

b. 1,956.8 is a sample mean because it is calculated from the data of the 40 election districts in Alaska.

c. To find the probability that a randomly selected district had fewer than 1,600 votes for the candidate, you need to standardize the value and use the standard normal distribution table. First, calculate the z-score using the formula z = (x - mean) / standard deviation. Plugging in the values, we get z = (1600 - 1956.8) / 572.3 = -0.621. Then, we can use the standard normal distribution table to find the probability associated with a z-score of -0.621, which is approximately 0.267.

d. To find the probability that a randomly selected district had between 1,800 and 2,000 votes for the candidate, you need to calculate the z-scores for both values and find the area between them on the standard normal distribution. Use the same formula as before to get z1 = (1800 - 1956.8) / 572.3 = -0.275 and z2 = (2000 - 1956.8) / 572.3 = 0.075. Then, use the standard normal distribution table to find the area between z1 and z2, which is approximately 0.161.

e. The 95th percentile represents the value below which 95% of the data falls. To find the 95th percentile for votes for the candidate, you can use the z-score associated with a cumulative probability of 0.95 on the standard normal distribution table. The z-score is approximately 1.645. Then, use the formula x = z * standard deviation + mean to calculate the value. Plugging in the values, we get x = 1.645 * 572.3 + 1956.8 ≈ 2,885 votes.

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80% of the times we are confident that the mean number of oocytes retrieved will fall in interval  ( 8.8 , 10.6 ).

A confidence interval is the probability that an estimate will fall in a particular range for a certain number of times.

From the given scenario, women are selected from the age group 36-40.

The mean number of oocytes retrieved from the 98 participants was 9.7 with an 80 % confidence level z ‑interval of ( 8.8 , 10.6 )

From the given condition we can conclude that if we repeat the experiment 80% of the times we are confident that the mean number of oocytes retrieved will fall in interval  ( 8.8 , 10.6 ).

Thus, the mean number of oocytes retrieved from the 98 participants in Group A was 9.7 with an 80 % confidence level has z ‑interval of ( 8.8 , 10.6 )

Learn more about Confidence interval, here:

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The question discusses a study in reproductive endocrinology involving hormone-assisted retrieval of oocytes for assisted reproduction, like IVF. Two hormones, likely follicle-stimulating hormone and luteinizing hormone, are used from day one to boost ovulation. The reported average number of oocytes and the confidence interval indicate the effectiveness of this treatment strategy.

The study described touches upon a field within biology known as reproductive endocrinology with a focus on hormone-assisted techniques in assisted reproduction like IVF (In Vitro Fertilization). The two hormones administered from day one are likely gonadotropins, consisting of follicle-stimulating hormone (FSH) and luteinizing hormone (LH), as per the common methods in IVF procedures. FSH supports the development of multiple follicles while LH triggers ovulation. Their administration significantly boosts the usual number of oocytes (eggs) produced in a woman's ovulation cycle.

Moreover, the mean number of oocytes (9.7) retrieved from the participants in Group A gives an indication of the effectiveness of the treatment strategy. The 80% confidence level z-interval of (8.8, 10.6) suggests that the actual mean number of oocytes retrieved for the overall population of women, aged 36-40 years, following this treatment strategy, is likely to lie within this range with an 80% probability.

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Answer:

The probability that the resident has both homeowner’s and automobile insurance with World Wide Insurance Company is 14% (P=0.1431).

Step-by-step explanation:

The probability of having homeowner’s insurance (H) with the company is P(H)=0.53.

The probability that, given that the resident has homeowner insurance with the company, also had a automobile insurance is P(A|H)=0.27.

We have to calculate P(A&H): probability of having automovile and homeowner:

[tex]P(A\&H)=P(H)*P(A|H)=0.53*0.27=0.1431[/tex]

Answer:

The probability that the resident has both homeowner’s and automobile insurance with World Wide Insurance Company is 0.143 OR 14.3%.

Step-by-step explanation:

We are given that:

53% of the residents had homeowner's insurance i.e. P(H) = 0.53

Of these people, 27% also had automobile insurance i.e. they had automobile insurance given that they had homeowner's insurance. So, P(A|H) = 0.27.

We need to find out the probability that the resident has both homeowner's and automobile insurance i.e. P(A and H) or P(A∩H). To compute P(A∩H) we will use the conditional probability formula:a

P(A|B) = P(A∩B)/P(B)

Here we have:

P(A|H) = P(A∩H)/P(H)

P(A∩H) = P(A|H) * P(H)

            = 0.27 * 0.53

P(A∩H) = 0.143

The probability that the resident has both homeowner’s and automobile insurance with World Wide Insurance Company is 0.143 OR 14.3%.

Answer:

x,y(6.-6)

Step-by-step explanation:

{x=-y

6(-y)-5y=66

-6-5y=66

11y=66

y=6

-x-y=0

x=-y;

x=-6

Answer:

Six more than half of a number is 20

Step-by-step explanation:

The given expression in word problem can be translated as:

Six more than half of a number is 20

Answer: B

Step-by-step explanation:

[tex]30(\frac{\pi}{180})=\frac{\pi}{6}[/tex]

Answer:

-1.64

Explanation:

Multiple Choice Answers that were not provided in the question:

a. 0.103 .

b. None of the above.

c. -4.16

d. -1.45

e. 2.86

f .-1.64

The provided data is as below:

             Student 1  Student 2  Student 3  Student 4  Student 5  Student 6

Pre- test    80              76              76              50             48              67

Post- test   75              86              87              60            48               68

Further Explanation:

                    Student 1  Student 2  Student 3  Student 4  Student 5  Student 6

Pre- test             80              76              76              50             48              67

Post- test            75              86              87              60            48               68

Pretest-Postest   5               -10              -11              -10            0                 -1

Calculating the mean of the difference (Pretest-postest) we get d bar = -4.5

Calculating the standard deviation  of the difference  (Pretest-postest) we get sd= 6.716.

Since sample score is under 30 and population standard deviation is unknown, we will use a tscore to find the standardized test statistic

t = dbar/(sd/√n) = -4.5/(6.716√6) = -1.642 ≈ -1.64

The test statistic is -1.64.

Using the normal approximation to the binomial, it is found that the correct option is:

The binomial distribution, which is the probability of exactly x successes on n repeated trials, with p probability of success on each trial(each trial either is a success or it is a failure), can be approximated to the normal if in a sample, there are at least 10 successes and at least 10 failures.

In this problem:

Thus, the correct option is:

A similar problem is given at https://brainly.com/question/24261244

Answer:

1) Null hypothesis:[tex]\mu = 120[/tex]  

Alternative hypothesis:[tex]\mu \neq 120[/tex]  

2) [tex]t=\frac{118.3-120}{\frac{3.7}{\sqrt{22}}}=-2.155[/tex]  

3) [tex] t_{cric}=\pm 2.08[/tex]

And the rejection zone of the null hypothesis would be [tex] |t_{calc}|>2.08[/tex]

4) Since our statistic calculated is higher than the critical value we have enough evidence to reject the null hypothesis at 5% of significance

5) Since we reject the null hypothesis of accuracy we have enough evidence to conclude at 5% of significance that the procedure is not accurate

6) Since we reject the null hypothesi we need to expect that the p value would be lower than the significance level provided and that means:

[tex] p_v <\alpha[/tex]

Step-by-step explanation:

Data given and notation  

[tex]\bar X=118.3[/tex] represent the sample mean

[tex]s=3.7[/tex] represent the sample standard deviation

[tex]n=22[/tex] sample size  

[tex]\mu_o =120[/tex] represent the value that we want to test

[tex]\alpha=0.05[/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)  

Part 1: State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the true mean is equal to 120 because that means accurate, the system of hypothesis would be:  

Null hypothesis:[tex]\mu = 120[/tex]  

Alternative hypothesis:[tex]\mu \neq 120[/tex]  

If we analyze the size for the sample is < 30 and 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".  

Part 2: Calculate the statistic

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

[tex]t=\frac{118.3-120}{\frac{3.7}{\sqrt{22}}}=-2.155[/tex]    

Part 3: Rejection region

We calculate the degrees of freedom given by:

[tex] df = n-1= 22-1 =21[/tex]

We need to find a critical value who accumulates [tex]\alpha/2 = 0.025[/tex] of the area in the tails of the t distribution with 21 degrees of freedom and we got:

[tex] t_{cric}=\pm 2.08[/tex]

And the rejection zone of the null hypothesis would be [tex] |t_{calc}|>2.08[/tex]

Part 4

Since our statistic calculated is higher than the critical value we have enough evidence to reject the null hypothesis at 5% of significance

Part 5

Since we reject the null hypothesis of accuracy we have enough evidence to conclude at 5% of significance that the procedure is not accurate

Part 6

Since we reject the null hypothesi we need to expect that the p value would be lower than the significance level provided and that means:

[tex] p_v <\alpha[/tex]

Answer:

0.0879 or 8.79 % is the process capability of the batch and the batch doesn't meet the control limits.

Step-by-step explanation:

mean of three readings=(1.023+0.999+1.025)/3= 1.0157

standard deviation=√((1.023-1.0157)² + (0.999-1.0157)²+ (1.025-1.0157)²)/3)

                             = 0.0163

Process Capability= min((USL-mean)/3SD, (Mean-LSL)/3SD)

(USL-mean)/3SD= (1.02-1.0157)/(3×0.0163)= 0.0879

(Mean-LSL)/3SD)= (1.0157-1.00)/(3×0.0163)= 0.321

Process capability=(0.0879,0.321)

0.0879 or 8.79 % is the process capability

The x-bar control chart and other statistical tools are used to assess whether product weights are within acceptable limits, thereby determining if quality standards are met and if equipment recalibration might be necessary.

The question involves evaluating if a batch of products (in this case, potentially cereal boxes, soda servings, lifting weights, apples, or lettuce) meets certain quality control standards, specifically relevant to the weights and measurements being within predefined control limits or tolerances. Using an x-bar control chart and statistical methods like hypothesis testing or calculating percent uncertainty, quality control specialists can determine whether a product's quality characteristic, such as weight, is within acceptable ranges, thereby assessing if equipment recalibration is needed or if a batch complies with quality standards.

For instance, if a new sample of items has weights that fall outside of the established control limits on the x-bar control chart, it would suggest that there may be an issue with the process control, indicating potential problems with the lot from which the sample was taken.

Concerning the exercises provided: In the case of the cereal boxes with a standard deviation higher than the acceptable limit, it suggests that recalibration might be needed. For the Class A apples, a hypothesis test at the specified significance levels would help determine compliance with weight tolerance. Calculating the percent uncertainty of a bag's weight informs us about the relative size of the uncertainty in measurements.

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Answer: [tex]y=8x[/tex]

Step-by-step explanation:

For this exercise it is important to remember that the equation of a line that passes through the origin (this is located at the point [tex](0,0)[/tex]), has the following form:

[tex]y=mx[/tex]

Where "m" is the slope of the line.

In this case, according to the information given in the exercise, you know that 8 million tons of plastic waste enters the world’s oceans every year, apprdoximately.

Then, let the independent variable "x" represents the number of years.

 Analizing the data given, you can identify that the slope of that line is the following:

[tex]m=8[/tex]

So, knowing the value of "m", you can subsitute them into the equation  [tex]y=mx[/tex], in order to get the equation that shows that situation.

This is:

[tex]y=8x[/tex]

Answer:

The p-value for the hypothesis test is 0.0042.

Step-by-step explanation:

We are given that the supervisor of a production line wants to check if the average time to assemble an electronic component is different from 14 minutes.

Assume that the population of assembly time is normally distributed with a standard deviation of 3.4 minutes. The supervisor times the assembly of 14 components, and finds that the average time for completion is 11.6 minutes.

Let [tex]\mu[/tex] = average time to assemble an electronic component.

SO, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 14 minutes  {means that the average time to assemble an electronic component is equal to 14 minutes}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 14 minutes   {means that the average time to assemble an electronic component is different from 14 minutes}

The test statistics that will be used here is One-sample z test statistics as we know about the population standard deviation;

                        T.S.  = [tex]\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)

where, [tex]\bar X[/tex] = sample average time for completion = 11.6 minutes

             [tex]\sigma[/tex] = population standard deviation = 3.4 minutes

             n = sample of components = 14

So, test statistics  =  [tex]\frac{11.6-14}{\frac{3.4}{\sqrt{14} } }[/tex]  

                               =  -2.64

Now, P-value of the hypothesis test is given by the following formula;

         P-value = P(Z < -2.64) = 1 - P(Z [tex]\leq[/tex] 2.64)

                                              = 1 - 0.99585 = 0.0042

Hence, the p-value for the hypothesis test is 0.0042.

The p-value for the hypothesis test is approximately 0.0082

To calculate the p-value for the hypothesis test, follow these steps:

1. State the null and alternative hypotheses:
  - Null hypothesis (\(H_0\)): The average assembly time is 14 minutes. \( \mu = 14 \)
  - Alternative hypothesis (\(H_1\)): The average assembly time is different from 14 minutes. \( \mu \ne 14 \)

2. Determine the test statistic:
  Since the population standard deviation (\(\sigma\)) is known, use the \( z \)-test for the mean. The test statistic is calculated using the formula:
[tex]\[ z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}} \][/tex]
  where:
  - \(\bar{x}\) is the sample mean,
  - \(\mu\) is the population mean under the null hypothesis,
  - \(\sigma\) is the population standard deviation,
  - \(n\) is the sample size.

  Given:
  [tex]\(\bar{x} = 11.6\) minutes,\\ \(\mu = 14\) minutes,\\ \(\sigma = 3.4\) minutes,\\ \(n = 14\).[/tex]

  Plug these values into the formula:
  [tex]\[ z = \frac{11.6 - 14}{3.4 / \sqrt{14}} \][/tex]

3. Calculate the value of the test statistic:
  [tex]\[ z = \frac{11.6 - 14}{3.4 / \sqrt{14}} = \frac{-2.4}{3.4 / \sqrt{14}} \approx \frac{-2.4}{0.9087} \approx -2.64 \][/tex]

4. Find the p-value:
  The p-value for a two-tailed test is calculated by finding the probability that the test statistic is at least as extreme as the observed value, under the null hypothesis.

  [tex]\[ p\text{-value} = 2 \times P(Z \leq z) \][/tex]

  Since we have a \( z \)-score of -2.64, we look up the cumulative probability for \( Z = -2.64 \) in the standard normal distribution table or use a calculator to find:
  [tex]\[ P(Z \leq -2.64) \approx 0.0041 \][/tex]

  Therefore:
  [tex]\[ p\text{-value} = 2 \times 0.0041 = 0.0082 \][/tex]

5. Interpret the results:
  Compare the p-value to the significance level (\(\alpha\)) to make a decision. Typically, \(\alpha\) is set at 0.05. If the p-value is less than \(\alpha\), we reject the null hypothesis.

  In this case:
  [tex]\[ p\text{-value} = 0.0082 \][/tex]

  Since \(0.0082 < 0.05\), we reject the null hypothesis. There is significant evidence to suggest that the average assembly time is different from 14 minutes.

So, the p-value for the hypothesis test is approximately 0.0082.

Answer:

The answer is 0.75.

Step-by-step explanation:

To use probability of a complement event, we need to find the situation where none of the couples are sitting next to each other which can happen either two husbands are sitting in the seats 2 and 3 or two wives are sitting in the seats 2 and 3. Also in the first scenario, the wives would need to be sitting at the opposite ends to their husbands and vice versa for the second scenario.

So there are in total 4 scenarios where no couple is sitting next to each other.

There are a total of 16 different ways that they can be seated so the probability of compelement is 16 - 4 = 12, which is 3/4 of the total, meaning that the probability of at least one of the wives sittting next to her husband is 0.75 or 75%.

I hope this answer helps.

The question is faulty written. I'll solve it assuming values for one variable and provide the answer to guide the student in their own question

Answer:

x=t

y=-1-9t

Step-by-step explanation:

Parametric Equations

Given an explicit relation between variables x and y, we can find expression for both of them in term of a third parameter t, such as

x=f(t)

y=g(t)

provided the main relation holds.

we have the equation

9x+y=-1

There are infinitely many forms to find parametric expressions for the variables, let's assume

x=t

Solving the equation for y

y=-1-9x=-1-9t

Thus the parametric equations are

x=t

y=-1-9t

Answer:

a)   32.57%

b)   0.9967

c)   5.3285 times.

Step-by-step explanation:

a. Return on sales is a simple ratio that is calculated by dividing the operating profit/income  by the net sales revenue.

-Given net sales revenue is $20,941 and the operating income is $6,821:

[tex]Return \ on \ sales(ROS)=\frac{Operating \ Income}{Net \ Sales \ Revenue}\\\\=\frac{6821}{20941}\\\\=0.3257\\\\=32.57\%[/tex]

Hence, the return on sales is 32.57%

b. Current ratio is a simple ratio that compares the current assets to the current liabilities.

-Given that current assets=$7,296 and current liabilities=$7,320, the current ratio is calculated as below:

[tex]Current \ Ratio=\frac{Current \ Assets}{Current \ Liabilities}\\\\=\frac{7296}{7320}\\\\=0.9967[/tex]

Hence, the current ratio is 0.9967

c. Inventory turnover is a measure of the frequency with which a company's goods is used or sold and subsequently restocked in given period.

-It's calculated by dividing the cost of goods sold by the average invenory as below:

[tex]Inventory \ Turnover=\frac{Cost \ of \ goods \ sold}{mean \ Invenory}\\\\\\=\frac{7055}{1324}\\\\=5.3285\ times[/tex]

Hence, the inventory turnover is 5.3285 times.

The calculated ratios for ABC Inc. are: Return on Sales of 19.3%, a Current Ratio of 0.997, and an Inventory Turnover of 5.33.

To calculate the ratios requested, we'll be using the financial data from ABC Inc.'s income statement and balance sheet.

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Answer:

Step-by-step explanation:

find attached the solution

Answer:

Solution (x, y, λ) = (2, 2, - 6)

Step-by-step explanation:

From the above information given:

3x + λ = 0............ eqn (1)

3y + λ = 0 ........... eqn (2)

x + y − 4 = 0 ......... eqn (3)

Now, from equation 1 and 2:

x= - λ / 3

y= - λ / 3

Substitute the values of X and y into equation 3

-λ/ 3 - λ/ 3 - 4 =0

-λ - λ - 12= 0

-2λ - 12= 0

-2λ = 12

λ = - 6

x= - λ/ 3

x = - (- 6) / 3

x= 2

y= - λ/3

y= - (-6)/3

y= 2

Solution (x, y, λ) = (2, 2, - 6)

Therefore,

x = 2

y= 2

λ = - 6

Answer:

[tex]v = \pi {r}^{2} \frac{h}{3} \\ \: \: \: \: = \pi \times 20 \frac{40}{3} \\ \: \: \: \: = 16755.16 {cm}^{3} [/tex]

hope this helps you

Answer:

You can get it by doing this

Step-by-step explanation:

The Probability

Answer:

0.08 percent chance or 1/12

Answer:

$10.32 is the sales tax.

$139.32 is the total price.

Step-by-step explanation:

Sales tax is 8% of the original price.

First, change the percentage into a decimal, by moving the decimal point to the left two place values: 8% = 0.08

Next, multiply 129 with 0.08:

129 x 0.08 = 10.32

$10.32 is the sales tax.

Then, add 10.32 to the original price:

10.32 + 129 = 139.32

$139.32 is the total price.

Answer:

f(x)= 3x + 1

Step-by-step explanation:

Let's set the unknown variable as b, since it's a linear equation.

Using the point given (-3, -8), we can find b by plugging in the known numbers and solving.

-8 = -3 (3) + b

-8 = -9 + b

b = 1

If you want, you can check it by forming the complete equation and plugging in -3.

f(x)= 3x + 1

f(-3) = -9 + 1

f(-3) = -8 = -8

I hope this helped!

Answer:

a. What is the standard error of the sample proportion who find this offer attractive? =  0.0351

b. What is the probability that the sample proportion is more than 0.15? = 0.9222

c. What is the probability that the sample proportion is between 0.18 and 0.22? =  0.4314

Step-by-step explanation:

see attachment for explanation

Answer:

Step-by-step explanation:

Given that,

p = 0.20

1 - p = 1 - 0.20 = 0.80

n = 130

\mu\hat p = p = 0.20

A) \sigma \hat p =  \sqrt[p( 1 - p ) / n] = \sqrt [(0.20 * 0.80 ) / 130] = 0.0351

B) P( \hat p > 0.15) = 1 - P( \hat p < 0.15)

= 1 - P(( \hat p - \mu \hat p ) / \sigma \hat p < (0.15 - 0.20) / 0.0351 )

= 1 - P(z < -1.42)

Using z table

= 1 - 0.0778

= 0.9222

C) P(0.18 < \hat p < 0.22)

= P[(0.18 - 0.20) / 0.0351 < ( \hat p - \mu \hat p ) / \sigma \hat p < (0.22 - 0.20) / 0.0351]

= P(-0.57 < z < 0.57)

= P(z < 0.57) - P(z < -0.57)

Using z table,    

= 0.7157 - 0.2843

= 0.4314

Given:

Given that the radius of the circle is √98 units.

The circle is centered at the point (5.9, 6.7)

We need to determine the equation of the circle.

Equation of the circle:

The general form of the equation of the circle is given by

[tex](x-h)^2+(y-k)^2=r^2[/tex]

where (h,k) is the center and r is the radius of the circle.

Substituting the center point (h,k) = (5.9, 6.7) and r = √98, we get;

[tex](x-5.9)^2+(y-6.7)^2=(\sqrt{98})^2[/tex]

Simplifying, we get;

[tex](x-5.9)^2+(y-6.7)^2=98[/tex]

Thus, the equation of the circle is [tex](x-5.9)^2+(y-6.7)^2=98[/tex]

the equation of the circle with radius square root of 98 centered at (5.9, 6.7) is: [tex](x - 5.9)^2 + (y - 6.7)^2 = 98[/tex]

We know that the equation of circle is given by the formula:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

here h and k are the x and y coordinates of the center of circle and r is the radius. It is given to us that:

Radius = √98 units

Center at (5.9, 6.7)

Putting values into the equation we get:

[tex](x - 5.9)^2 + (y - 6.7)^2 = (\sqrt{98})^2\\\\ (x - 5.9)^2 + (y - 6.7)^2 = 98[/tex]

Therefore, the equation of the circle with radius square root of 98 centered at (5.9, 6.7) is: [tex](x - 5.9)^2 + (y - 6.7)^2 = 98[/tex]

Answer:

The mean of the sampling distribution is 20 and the standard deviation is 2.89.

Step-by-step explanation:

The Central Limit Theorem estabilishes 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.

Population:

Mean 20, standard deviation of 5.

Sampling distribution:

3 rounds

Mean = 20

[tex]s = \frac{5}{\sqrt{3}} = 2.89[/tex]

The mean of the sampling distribution is 20 and the standard deviation is 2.89.

Final answer:

The mean of Paul's sampling distribution is 20 points per round, and the standard deviation is approximately 2.89 points per round, calculated using the formula for the standard error of the mean.

Explanation:

The scenario involves a sampling distribution of the mean scores over random samples of 3 rounds from Paul's video game scores. To calculate the mean and standard deviation (sd) of the sampling distribution, we use the following formulas:

Therefore, the mean of the sampling distribution is 20, and the standard deviation is approximately 2.89.

Answer:

20 times

Step-by-step explanation:

8, 18, 28, 38, 48, 58, 68, 78, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 98

1     2    3   4   5   6      7   8     9   10  11    12   13   14   15   16  17 18 19 20

Answer:

x=2

Step-by-step explanation:

To solve, we need to isolate the variable (x)

To do this, we must get all the variables to one side of the equation, and all the numbers to the other

3x+3= -2x+13

Add 2x to both sides to "reverse" the subtraction

5x+3=13

Subtract 3 from both sides to "reverse" the addition

5x=10

Divide both sides by 5 to "reverse" the multiplication

x=2