Given f(x) = x² - 10x + 22, what is the range of f?

Answer:

42

Step-by-step explanation:

work backwards And use the opposite operation

start with 8 x 4 = 32 + 40 = 72/2 = 36 + 6 = 42

The problem is an Optimization problem in Calculus that is solved by representing the volume of the open box in terms of a single variable using the fixed cost. With the volume equation, we can use calculus to find the optimal dimensions.

The question is about maximizing the volume of an open box given a fixed cost and considering that the base of the box is 1.5 times as expensive as the sides. This problem comes under the branch of mathematics known as Optimization in Calculus. The volume V of an open box (a box without a top) is given by the product of its length, width, and height (V = lwh).

In this problem, the total cost is fixed, hence, the sum of the cost of the base and the cost of the sides is a constant. We can say that cost = C = (Base Cost) + (Sides Cost) = 1.5lw + 2.0lh + 2.0wh. We can express the width w in terms of l and h using the cost equation, and then substitute in the volume equation to write V in terms of a single variable. This enables the use of calculus to optimize the volume. It is beyond the scope of this answer to give a complete solution, but essentially, you would differentiate to obtain an equation, and solve for the optimal dimensions.

https://brainly.com/question/37742146

#SPJ2

Answer:

[tex]19.1-3.355\frac{1.5}{\sqrt{9}}=17.42[/tex]    

[tex]19.1+3.355\frac{1.5}{\sqrt{9}}=20.78[/tex]    

And the best option would be:

C. [17.42,20.78]

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

[tex]\bar X=19.1[/tex] represent the sample mean

[tex]\mu[/tex] population mean (variable of interest)

s=1.5 represent the sample standard deviation

n=9 represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

In order to calculate the critical value [tex]t_{\alpha/2}[/tex] we need to find first the degrees of freedom, given by:

[tex]df=n-1=9-1=8[/tex]

Since the Confidence is 0.99 or 99%, the value of [tex]\alpha=0.01[/tex] and [tex]\alpha/2 =0.005[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,8)".And we see that [tex]t_{\alpha/2}=[/tex]

Now we have everything in order to replace into formula (1):

[tex]19.1-3.355\frac{1.5}{\sqrt{9}}=17.42[/tex]    

[tex]19.1+3.355\frac{1.5}{\sqrt{9}}=20.78[/tex]    

And the best option would be:

C. [17.42,20.78]

Final answer:

To summarize data in a significance test for two different treatments with a quantitative response variable, the mean and standard deviation for each treatment group are computed separately to look for statistically significant differences.

Explanation:

When conducting a significance test to determine if there is a difference between two treatments with a quantitative response variable, and treatments are given to different experimental units, we summarize the data by computing the mean and standard deviation of each treatment group separately. This approach involves comparing the two sets of data from the treatment groups to see if there is a statistically significant difference in their means, which could suggest an effect of the treatments. This methodology is part of inferential statistics, where researchers use the collected sample data to make inferences about the population from which the sample was drawn.

Answer:

5/6

Step-by-step explanation:

2/3=4/6

4/6+1/6=5/6

Answer:

That would be 5/6

Step-by-step explanation:

You multiply the denominator and the numerator by 2 to get a common denominator of 6. You add the 4 to the 1 to get 5/6

9514 1404 393

Answer:

  (x, y, z) = (20, 4, 5)

Step-by-step explanation:

The last two equations allow y and z to be expressed in terms of x, so we have ...

  3x +2(5y) -3(4z) = 40

  3x +2(x) -3(x) = 40

  x = 20 . . . . . . . . . . . . divide by the coefficient of x

  y = 20/5 = 4

  z = 20/4 = 5

The solution is (x, y, z) = (20, 4, 5).

Answer:  

We are 85% confident that the proportion of adults who dreaded valentines day is within the range of 8.8% to 21.2%.

Step-by-step explanation:  

Proportion of adults who dreaded valentines day = 15% = 0.15

The margin of error with 85% confidence = 6.2% = 0.062

The confidence interval is given by

p ± margin of error

0.15 ± 0.062

Lower limit = 0.15 - 0.062

Lower limit = 0.088

Lower limit = 8.8%

Upper limit = 0.15 + 0.062

Upper limit = 0.212

Upper limit = 21.2%

So it means that we are 85% confident that the proportion of adults who dreaded valentines day is within the range of 8.8% to 21.2%.

Answer:

The minimum sample size required is 25 so that margin of error is no more than 3 minutes.  

Step-by-step explanation:

We are given the following in the question:

Mean, μ = 42 minutes

Standard Deviation, σ = 9 minutes.

We want to build a 90% confidence interval such that margin of error is no more than 3 minutes.

Formula for margin of error:

[tex]z_{critical}\times \dfrac{\sigma}{\sqrt{n}}[/tex]

[tex]z_{critical}\text{ at}~\alpha_{0.10} = 1.64[/tex]

Putting values, we get.

[tex]z_{critical}\times \dfrac{\sigma}{\sqrt{n}}\leq 3\\\\1.64\times \dfrac{9}{\sqrt{n}}\leq 3\\\\\dfrac{1.64\times 9}{3}\leq \sqrt{n}\\\\4.92\leq \sqrt{n}\\\Rightarrow n\geq 24.2064\approx 25[/tex]

Thus, the minimum sample size required is 25 so that margin of error is no more than 3 minutes.

Answer:

B

Step-by-step explanation:

Answer:

The base area is the total area of D

The lateral area is the total area of A, B, and C

The surface area is the total area of A, B, C, and D.

Answer:

(d) the base area is the total area

Explain: because i got it right on the test

Answer:

y = 8

Step-by-step explanation:

2y + 3 = 19

2y = 19 - 3

2y = 16

y = 16/2

y = 8

Hopefully this help u

Answer: y = 8

Step-by-step explanation: To solve for y, we must first isolate the term containing y which in this problem is 2y.

Since 3 is being added to 2y, we subtract 3 from

both sides of the equation to isolate the 2y.

On the left, the +3 and -3 cancel

out and on the right, 19 - 3 is 16.

So we have 2y = 16.

Now we can finish things off by just dividing

both sides of the equation by 2.

On the left the 2's cancel and on

the right, 16 divided by 2 is 8.

So y = 8.

Answer:

By the Chebyshev Theorem, 75% probability of a randomly selected state having between 21 and 53 multi-million dollars

Step-by-step explanation:

We have no information about the distribution, so we use the Chebyshev's theorem to solve this question.

Chebyshev Theorem:

75% of the data within 2 standard deviations of the mean.

89% of the data within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 37

Standard deviation = 8

What is the probability of a randomly selected state having between 21 and 53 multi-million dollars

21 = 37 - 2*8

So 21 is 2 standard deviations below the mean.

53 = 37 + 2*8

So 52 is 2 standard deviations above the mean.

By the Chebyshev Theorem, 75% probability of a randomly selected state having between 21 and 53 multi-million dollars

Answer:

Expected value of the total volume shipped = 97,650 ft³

Variance of the total volume shipped = 15,183,265

Standard deviation = 3896.6 ft³

Step-by-step explanation:

The mean of number of type 1, 2 and 3 containers in a week

μ₁ = 230, μ₂ = 240, μ₃ = 120

The standard deviations for the number of type 1, 2 and 3 containers in a week

σ₁ = 11, σ₂ = 12, σ₃ = 7

When independent distributions are combined, the combined mean and combined variance are given through the relation

Combined mean = Σ λᵢμᵢ

(summing all of the distributions in the manner that they are combined)

Combined variance = Σ λᵢ²σᵢ²

(summing all of the distributions in the manner that they are combined)

Volume of each container type

λ₁ = 27 ft³

λ₂ = 125 ft³

λ₃ = 512 ft³

Distribution of total volume shipped

= 27X₁ + 125X₂ + 512X₃

Expected value = Combined Mean = 27μ₁ + 125μ₂ + 512μ₃

= (27×230) + (125×240) + (512×120) = 590

Combined Variance = 27²σ₁² + 125²σ₂² + 512²σ₃²

= (27² × 11²) + (125² × 12²) + (512² × 7²)

= 88,209 + 2,250,000 + 12,845,056

= 15,183,265

Standard deviation = √(15,183,265) = 3896.6 ft³

Hope this Helps!!!

Answer:

E(rP) = 4% + 5.50% x β(M1) + 10.92% x β(M2)

Step-by-step explanation:

let us recall from the following statement:

The  two independent economic factors are M1 and M2

Th risk free rate = 4%

The standard deviation of all stocks of  independent firm specific components is =49%

P = portfolios for A and B

Now,

What is the expected relationship of return-beta

The Expected return-beta relationship E(rP) =  % +  βp₁ +  βp₂

E(rA) = 4% + 1.6 * M1 + 2.4* M2 = 39%

E(rB) = 4% + 2.3 * M1 + (-0.7)* M2 = 9%

Therefore

Solving for M1 and M2 using excel solver, we have M1 = 5.50% and M2 = 10.92%

E(rP) = 4% + 5.50% x β(M1) + 10.92% x β(M2)

The question pertains to finance and investment analysis. It emphasizes the CAPM model, which combines systematic risk measured by beta and market risk premium to calculate expected returns on portfolios. It also highlights that diversification reduces firm-specific risks.

The question deals with the concept of portfolio return, beta coefficients, and firm-specific risk, which are important aspects of finance and investment analysis. The expected return on portfolios A and B, can be calculated using the CAPM model, which states that expected return equals the risk-free rate plus the portfolio's beta (which measures systematic risk) multiplied by the market risk premium (difference between the expected market return and the risk-free rate). To compute this, the beta coefficients need to be multiplied with their respective economic factors, and the results obtained are added together.

For portfolio A, the expected return would be calculated like this: Return = Risk-Free rate + β1*M1 + β2*M2 = 4 + (1.6 * M1) + (2.4 * M2).

For portfolio B, the calculation would be similar: Return = Risk-Free rate + β1*M1 + β2*M2 = 4 + (2.3 * M1) - (0.7 * M2). The negative beta on M2 indicates that the portfolio's return would decrease when M2 increases, hence it has an inverse relationship with the portfolio return. The independent firm-specific component would not affect the return as per the assumption that the portfolios are well diversified; diversification reduces, but not completely eliminates, the firm-specific risk.

https://brainly.com/question/32359578

#SPJ3

Answer:

[tex]t=\frac{88.8-93}{\frac{26.6}{\sqrt{73}}}=-1.349[/tex]    

[tex]p_v =P(t_{(72)}<-1.349)=0.0908[/tex]  

If we compare the p value and the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to fail reject the null hypothesis, and we can't concluce that the true mean is less than 93 min at 5% of signficance.  

Step-by-step explanation:

Data given and notation  

[tex]\bar X=88.8[/tex] represent the sample mean

[tex]s=26.6[/tex] represent the sample standard deviation for the sample  

[tex]n=73[/tex] sample size  

[tex]\mu_o =93[/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)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the true mean i lower than 93 min, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \geq 93[/tex]  

Alternative hypothesis:[tex]\mu < 93[/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{88.8-93}{\frac{26.6}{\sqrt{73}}}=-1.349[/tex]    

P-value

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

[tex]df=n-1=73-1=72[/tex]  

Since is a one side test the p value would be:  

[tex]p_v =P(t_{(72)}<-1.349)=0.0908[/tex]  

Conclusion  

If we compare the p value and the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to fail reject the null hypothesis, and we can't concluce that the true mean is less than 93 min at 5% of signficance.  

The null hypothesis is that the mean repair time for the new model is equal to the mean repair time for the previous model. The alternative hypothesis is that the mean repair time for the new model is less than the mean repair time for the previous model. By performing a one-sample t-test, we compare the sample mean repair time to the population mean repair time. Using the calculated t-statistic and the critical t-value, we determine whether to reject or fail to reject the null hypothesis.

The null hypothesis, denoted as H0, states that the mean repair time for the new model of copying machine is equal to the mean repair time for the previous model (93 minutes). The alternative hypothesis, denoted as H1, states that the mean repair time for the new model is less than 93 minutes.

To test these hypotheses, we can perform a one-sample t-test. Using the given sample data, we calculate the t-statistic as:

t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))

Using the t-distribution table or a calculator, we find the critical t-value at a significance level of 0.05 and degrees of freedom (sample size - 1). If the calculated t-statistic is less than the critical t-value, we reject the null hypothesis and conclude that the new model has a lower mean repair time. Otherwise, we fail to reject the null hypothesis.

In this case, the calculated t-statistic is:

t = (88.8 - 93) / (26.6 / sqrt(73)) ≈ -1.34

With 72 degrees of freedom, the critical t-value at α = 0.05 is -1.666. Since the calculated t-statistic (-1.34) is greater than the critical t-value (-1.666), we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that the new model of copying machine has a significantly lower mean repair time than the previous model.

https://brainly.com/question/34171008

#SPJ11

Given:

Given that the triangle ABC is similar to triangle FGH.

We need to determine the value of x.

Value of x:

Since, the triangles are similar, then their sides are proportional.

Thus, we have;

[tex]\frac{AC}{FH}=\frac{AB}{GF}=\frac{BC}{GH}[/tex]

Let us consider the proportion [tex]\frac{AB}{GF}=\frac{BC}{GH}[/tex] to determine the value of x.

Substituting AB = 9 cm, GF = 13.5 cm, BC = 15 cm and GH = x, we get;

[tex]\frac{9}{13.5}=\frac{15}{x}[/tex]

Cross multiplying, we get;

[tex]9x=15 \times 13.5[/tex]

[tex]9x=202.5[/tex]

 [tex]x=22.5 \ cm[/tex]

Thus, the value of x is 22.5 cm

Hence, Option F is the correct answer.

Answer:

22.5

Step-by-step explanation:

Answer: I think the answer is B. I don't fully understand the question but it seems like that would be the answer. You might double check though.

Step-by-step explanation:

Answer:

-2/7 0r 2/-7 or the negative sign is in the middle

Step-by-step explanation:

(-3/4)(-4/7)= 3/7

3/7 x -2/3= -2/7

Answer:

[tex]z = \frac{21.3-21}{\frac{1.2}{\sqrt{50}}}= 1.77[/tex]

Step-by-step explanation:

Data given and notation  

[tex]\bar X=21.3[/tex] represent the sample mean

[tex]\sigma=1.2[/tex] represent the population standard deviation

[tex]n=50[/tex] sample size represent the value that we want to test

[tex]\alpha[/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 mean is higher than 21, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \leq 21[/tex]  

Alternative hypothesis:[tex]\mu > 21[/tex]  

If we analyze the size for the sample is > 30 and we know the population deviation so is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:  

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

z-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]z = \frac{21.3-21}{\frac{1.2}{\sqrt{50}}}= 1.77[/tex]

Answer:

The confidence interval for the proportion of students supporting the fee increase

( 0.77024, 0.81776)

Step-by-step explanation:

Explanation:

Given data a survey of an urban university (population of 25,450) showed that 883 of 1,112 students sampled supported a fee increase to fund improvements to the student recreation center.

Given sample size 'n' = 1112

Sample proportion 'p' = [tex]\frac{883}{1112} = 0.7940[/tex]

                           q = 1 - p = 1- 0.7940 = 0.206

The 95% level of confidence intervals

The confidence interval for the proportion of students supporting the fee increase

[tex](p-z_{\alpha } \sqrt{\frac{pq}{n} } ,p + z_{\alpha } \sqrt{\frac{pq}{n} } )[/tex]

The Z-score at 95% level of significance =1.96

[tex](0.7940-1.96\sqrt{\frac{0.7940 X 0.206}{1112} } ,0.7940 + 1.96 \sqrt{\frac{0.7940 X 0.206}{1112} } )[/tex]

(0.7940-0.02376 , 0.7940+0.02376)

( 0.77024, 0.81776)

Conclusion:-

The confidence interval for the proportion of students supporting the fee increase

( 0.77024, 0.81776)

Answer:

38,38,380

Step-by-step explanation:

GIVEN: A club is considering changing its laws. In an initial straw vote on the issue, [tex]24[/tex] of the [tex]40[/tex] members of the club favored the change and [tex]16[/tex] did not. A committee of six is to be chosen from the [tex]40[/tex] club members to devote further study to the issue.

TO FIND: How many committees of six can be formed from the club membership.

SOLUTION:

Total number of members [tex]=40[/tex]

Total members to be chosen [tex]=6[/tex]

To select committee of [tex]6[/tex] members from [tex]40[/tex] [tex]=^{40}C_6[/tex]

                                                                       [tex]=\frac{40!}{34!6!}[/tex]

                                                                      [tex]=38,38,380[/tex]

Hence 38,38,380 different committee can be formed.

The subject of this question is Science in Middle School. The student is learning about scientific models by making a model of air flow in their classroom or room in their house.

The subject of this question is Science and the grade level is Middle School. In this question, the student is learning about scientific models by making a model of how air flows through their classroom or a room in their house. The student can use this activity to gain a better understanding of how air moves in closed spaces and the factors that affect its flow.

https://brainly.com/question/18893139

#SPJ12

Answer:

B C E are the answers

Step-by-step explanation:

hope it helps

Only the equations -1(x/4) + 3/4 = 12 and (-x/4) + 3/4 = 12 are equivalent to the original equation. The other equations provided do not hold the same properties of distribution and are not equivalent to the original equation.

When comparing these equations to the original, we must take into consideration the properties of distribution, a crucial component of algebra. The original equation is -1/4(x) + 3/4 = 12. Let's go through the options one by one:

https://brainly.com/question/34191741

#SPJ3

Answer:

seven and six hundred thirty thousandths

Step-by-step explanation:

the decimal point is when you say and when reading it

The representation of 7.630 in word form is; Seven and six hundred thirty thousandths.

The place values on left of decimal point start as ones, tens, hundreds, and so on.

The place value on right of decimal point starts from point and goes to right as tenths, hundreths and so on

The tens means multiply by 10

The tenth means tenth part of that digit which is that digit divided by 10

Place value of decimal numbers;

The given number is; 7.630

The given number can be written as;

7 and 0.630

Hence, the number can be pronounced as Seven and 630 thousandths.

However, we have,

Seven and six hundred thirty thousandths.

Hence, The representation of 7.630 in word form is; Seven and six hundred thirty thousandths.

Read more on place value;

brainly.com/question/627658

#SPJ5

Answer:

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

The 90% confidence interval for this case would be (38.01, 44.29) and is given.

The best interpretation for this case would be: We are 90% confident that the true average is between $ 38.01 and $ 44.29 .

And the best option would be:

The store manager is 90% confident that the average amount spent by all customers is between S38.01 and $44.29

Step-by-step explanation:

Assuming this complete question: Which statement gives a valid interpretation of the interval?

The store manager is 90% confident that the average amount spent by the 36 sampled customers is between S38.01 and $44.29.

There is a 90% chance that the mean amount spent by all customers is between S38.01 and $44.29.

There is a 90% chance that a randomly selected customer will spend between S38.01 and $44.29.

The store manager is 90% confident that the average amount spent by all customers is between S38.01 and $44.29

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Solution to the problem

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

The 90% confidence interval for this case would be (38.01, 44.29) and is given.

The best interpretation for this case would be: We are 90% confident that the true average is between $ 38.01 and $ 44.29 .

And the best option would be:

The store manager is 90% confident that the average amount spent by all customers is between S38.01 and $44.29

Answer:

4=c

Step-by-step explanation:

7c + 3 - 7c = 3c - 9​

Combine like terms

7c-7c+3 = 3c-9

3 = 3c-9

Add 9 to each side

3+9 = 3c-9+9

12 = 3c

Divide each side by 3

12/3 = 3c/3

4 =c

Answe

c=−4/3

Step-by-step explanation:

Answer:

its c I just id the test

Step-by-step explanation:

Given:

Given that the graph OACE.

The coordinates of the vertices OACE are O(0,0), A(2m, 2n), C(2p, 2r) and E(2t, 0)

We need to determine the midpoint of EC.

Midpoint of EC:

The midpoint of EC can be determined using the formula,

[tex]Midpoint=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]

Substituting the coordinates E(2t,0) and C(2p, 2r), we get;

[tex]Midpoint=(\frac{2t+2p}{2},\frac{0+2r}{2})[/tex]

Simplifying, we get;

[tex]Midpoint=(\frac{2(t+p)}{2},\frac{2r}{2})[/tex]

Dividing, we get;

[tex]Midpoint=(t+p,r)[/tex]

Thus, the midpoint of EC is (t + p, r)

Hence, Option A is the correct answer.

Answer:

The mean calculated for this case is [tex]\bar X=584[/tex]

And the 95% confidence interval is given by:

[tex]584-2.776\frac{86.776}{\sqrt{5}}=476.271[/tex]    

[tex]584+2.776\frac{86.776}{\sqrt{5}}=691.729[/tex]    

So on this case the 95% confidence interval would be given by (476.271;691.729)    

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

[tex]\bar X[/tex] represent the sample mean for the sample  

[tex]\mu[/tex] population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

In order to calculate the mean and the sample deviation we can use the following formulas:  

[tex]\bar X= \sum_{i=1}^n \frac{x_i}{n}[/tex] (2)  

[tex]s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}[/tex] (3)  

The mean calculated for this case is [tex]\bar X=584[/tex]

The sample deviation calculated [tex]s=86.776[/tex]

In order to calculate the critical value [tex]t_{\alpha/2}[/tex] we need to find first the degrees of freedom, given by:

[tex]df=n-1=5-1=4[/tex]

Since the Confidence is 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-T.INV(0.025,4)".And we see that [tex]t_{\alpha/2}=2.776[/tex]

Now we have everything in order to replace into formula (1):

[tex]584-2.776\frac{86.776}{\sqrt{5}}=476.271[/tex]    

[tex]584+2.776\frac{86.776}{\sqrt{5}}=691.729[/tex]    

So on this case the 95% confidence interval would be given by (476.271;691.729)    

Final answer:

The point estimate of the population mean of SAT math scores, calculated from the sample scores (570, 620, 710, 540, and 480), is 584.

Explanation:

The subject of this question is Mathematics, specifically focusing on statistics and the SAT examination scores. To calculate the point estimate for the given simple random sample of SAT Mathematics test scores (570, 620, 710, 540, and 480), we need to find the sample mean. This can be done by adding all the scores together and dividing by the number of students in the sample, which is five in this case.

Point Estimate calculation:

Add all the scores together: 570 + 620 + 710 + 540 + 480 = 2920

Divide by the number of students: 2920 / 5 = 584

The point estimate of the population mean of SAT math scores is 584.