"A sample of 64 hotels in Atlanta was selected in order to determine whether or not the average room price is significantly different from $110. The average price of the rooms in the sample was $112. The population standard deviation is known to be $16. Use a 0.05 level of significance. Use this information to answer Questions 16 to 19. What should be the appropriate null and alternative hypotheses for the purpose of your analysis?"

Answer:

A, B, D

Step-by-step explanation:

The linear parent function is a straight line with equation x=y, which means that it has a slope of 1 and goes through the origin. However, it does not go through quadrants 2 and 4, only 1 and 3. Hope this helps!

Answer:

$3,256.2

Step-by-step explanation:

First, we need to get 3% of 3,460. Find the decimal value of 3%:

3% -> [tex]\frac{3}{100}[/tex] -> 0.03

Next, lets multiply 3,460 by 0.03:

[tex]x=3,460(0.03)[/tex]

[tex]x=103.8[/tex]

Now subtract that number from 3,460:

[tex]3,460-103.8=3,356.2[/tex]

Lastly, lets take the $100 fee off of the number we just got:

[tex]3,356.2-100=3,256.2[/tex]

The new amount is $3,256.2

Answer:

3% fee is taken out of an initial amount of $3,460, and then a $100 fee is taken after that, leaving a new amount of $3,256.2.

explanation:

Answer:

The distribution is approximately normal.

The mean and standard deviation are 15 and 0.98 respectively.

Step-by-step explanation:

The population of the random variables X₁ and X₂ are distributed as follows:

[tex]X_{1}\sim (\mu_{1}=35, \sigma_{1}^{2}=3^{2})\\\\X_{2}\sim (\mu_{2}=20, \sigma_{2}^{2}=4^{2})[/tex]

Two independent random samples of sizes,

[tex]n_{1}=47\\\\n_{2}=54[/tex]

are selected form the two populations.

According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.  

Then, the mean of the sample means is given by,

[tex]\mu_{\bar x}=\mu[/tex]

And the standard deviation of the sample means is given by,

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]

Both the sample selected from the two populations are quite large, i.e. [tex]n_{1}=47>30\\\\n_{2}=54>30[/tex]

So, according to the central limit theorem the sampling distribution of sample means [tex]\bar X_{1}\ \text{and}\ \bar X_{2}[/tex] can be approximated by the Normal distribution.

Then, the distribution of [tex]\bar X_{1}[/tex] is:

[tex]\bar X_{1}\sim N(35,\ 0.44)[/tex]

And the distribution of [tex]\bar X_{2}[/tex] is:

[tex]\bar X_{2}\sim N(20,\ 0.54)[/tex]

If two random variables are normally distributed then their linear function is also normally distributed.

So, the distribution of [tex]\bar X_{1}\ - \bar X_{2}[/tex] is Normal and the shape of the distribution is bell-shaped.

The mean of the distribution of [tex]\bar X_{1}\ - \bar X_{2}[/tex] is:

[tex]E(\bar X_{1}\ -\ \bar X_{2})=E(\bar X_{1})-E(\bar X_{2})\\=35-20\\=15[/tex]

The standard deviation of the distribution of [tex]\bar X_{1}\ - \bar X_{2}[/tex] is:

[tex]SD(\bar X_{1}-\bar X_{2})=SD(\bar X_{1})+SD(\bar X_{2})\\=0.44+0.54\\=0.98[/tex]

*X₁ and X₂ are independent.

Thus, the mean and standard deviation are 15 and 0.98 respectively.

Answer:

20 seconds

Step-by-step explanation:

The least common multiple of 4 and 5 is 20.  So the two lights will blink at the same time every 20 seconds.

Based on the number of seconds it takes for each light to blink, they will both blink at 20 seconds.

The green light blinks every 4 seconds and the yellow, every 5 seconds.

The time that they will blink together depends on the lowest common multiple of both numbers.

Multiples of 4 = 4, 8, 12, 16, 20

Multiples of 5 = 5, 10, 15, 20

The lowest common multiple is 20 which means they will blink together after 20 seconds.

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Answer:

[tex]t=\frac{6.5-7}{\frac{2.1}{\sqrt{57}}}=-1.798[/tex]    

Critical value

The degreed of freedom are given by:

[tex]df=n-1=57-1=56[/tex]  

We are looking for a critical value in the t distribution with 56 degrees of freedom who accumulates 0.10 of the area in the left and we got:

[tex] t_{\alpha}= -1.297[/tex]

And since the calculated value is lower than the critical value we have enough evidence to reject the null hypothesis for this case and makes sense conclude that the true mean is less than 7 minutes

P value

The p value for this case would be given by:

[tex]p_v =P(t_{(56)}<-1.798)=0.0388[/tex]  

Since the p value is lower than the significance level provided of 0.1 we have enough evidence to conclude that the true mean is significantly lower than 7 minutes

Step-by-step explanation:

Information provided

[tex]\bar X=6.5[/tex] represent the sample mean for tje waiting times

[tex]s=2.1[/tex] represent the sample standard deviation

[tex]n=57[/tex] sample size  

[tex]\mu_o =7[/tex] represent the value to verify

[tex]\alpha=0.1[/tex] represent the significance level

t would represent the statistic

[tex]p_v[/tex] represent the p value

System of hypothesis

We want to verify if the true mean for this case is less than 7 minutes, the system of hypothesis for this case sre:  

Null hypothesis:[tex]\mu \geq 7[/tex]  

Alternative hypothesis:[tex]\mu < 7[/tex]  

Since we don;t know the population deviation the statistic for the t test is given by:

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

If we replace the info given we got:

[tex]t=\frac{6.5-7}{\frac{2.1}{\sqrt{57}}}=-1.798[/tex]    

Critical value

The degreed of freedom are given by:

[tex]df=n-1=57-1=56[/tex]  

We are looking for a critical value in the t distribution with 56 degrees of freedom who accumulates 0.10 of the area in the left and we got:

[tex] t_{\alpha}= -1.297[/tex]

And since the calculated value is lower than the critical value we have enough evidence to reject the null hypothesis for this case and makes sense conclude that the true mean is less than 7 minutes

P value

The p value for this case would be given by:

[tex]p_v =P(t_{(56)}<-1.798)=0.0388[/tex]  

Since the p value is lower than the significance level provided of 0.1 we have enough evidence to conclude that the true mean is significantly lower than 7 minutes

Following are the solution to the given question:

Given:

size [tex](n) = 58[/tex]

mean [tex]\mu = 7.4 \ minutes[/tex]

standard deviation [tex]\sigma = 2.3 \ minutes[/tex]

null and alternative hypotheses:

[tex]H_0 : \mu = 8 \ minutes\\\\H_a : \mu < 8 \ minutes\\\\[/tex]

Calculating the test statistic:

So, the observed value

Calculating the degrees of freedom:

[tex]\to 58 - 1 = 57[/tex]

Calculating the range of p-value:

Therefore the t is the critical value at the significance level that is 0.05 with of freedom is,

Therefore,

[tex]\to test \ statistic = -1.987 < -1.672[/tex]  rejecting the null hypothesis.

Therefore, the conclusion of the manager's claim is "True".

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Answer: A. Mean.

Explanation:

Mean is the only measure of central tendency that is always affected by an outlier. Mean, the average is the most popular measure of central tendency.

The mean is strongly influenced by outliers because it is the average of the scores and it is not resistant.

Answer:

A) mean

Step-by-step explanation:

Mean is a measure of central tendency, it is the sum of all data divided by the number of data. Because the mean take into consideration each of the data in its calculations, it is generally affected by outliers (extremely high or low values)

Answer:

  2√11

Step-by-step explanation:

The square of the hypotenuse (h) of the smaller triangle is given by the Pythagorean theorem:

  h² = 6² +8² = 100

The length of x is given by that same theorem:

  h² +x² = 12²

  x² = 12² -h² = 144 -100 = 44 . . . . . subtract h², fill in its value

  x = √44 . . . . . . . . take the square root

  x = 2√11 . . . . . . . simplify the root

The volume of Christina's cube-shaped coin bank is calculated by cubing the length of one of its sides, which is 7 inches. The volume is therefore 7 × 7 × 7, or 343 cubic inches.

The volume of Christina's cube-shaped coin bank can be calculated using the formula for the volume of a cube, which is Volume = side × side × side. As all sides of a cube are equal and the coin bank is 7 inches wide and 7 inches tall, we can calculate the volume by multiplying 7 inches by 7 inches by 7 inches.

Calculation:

Volume = 7 in. × 7 in. × 7 in. = 343 cubic inches

Hence, the volume of Christina's coin bank is 343 cubic inches.

Final answer:

The volume of Christina's cube-shaped coin bank is calculated using the cube volume formula and is found to be 343 cubic inches.

Explanation:

To calculate the volume of Christina's coin bank, we use the formula for the volume of a cube, which is Volume = side³, where 'side' is the length of one side of the cube. Since the coin bank is 7 inches wide and 7 inches tall, each side is 7 inches. Thus, the volume of the coin bank is:

Volume = 7 in. × 7 in. × 7 in. = 343 in.³

Therefore, Christina's coin bank has a volume of 343 cubic inches.

Answer:

48% was sold

Step-by-step explanation:

Let the percent sold be x

x/100 * 150 = 72

(This equation basically means...what percentage of 150 bundles will give us 72 bundles remaining? and that's the answer we need)

Simplifying...

150x/100 = 72

3x/2 = 72

3x = 144

x = 48%

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached image below to see the step by step explanation to the question above.

To find the p-value from the given data in Excel, populate your data in Excel sheet into various columns for each variable. Then, use the 'Regression' tool under 'Data Analysis' in the 'Data' tab, selecting the appropriate ranges for dependent and independent variables. Ensure that the 'P-Values' box is checked before clicking 'OK'. Excel will then generate the regression analysis with the p-value.

In Excel, you can perform regression analysis to deduce the p-value from this data using the following steps:

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Answer:

We conclude that the reaction time is increased or remains same by frequent alcohol use.

Step-by-step explanation:

We are given that a substance abuse researcher wants to know whether reaction time is decreased by frequent alcohol use. He randomly selects 164 alcoholics and finds that their mean reaction time (in ms) to a stimulus equals 283.

Reaction times to the stimulus in the general population are distributed normally with a mean equal to 281 and a standard deviation equal to 28.

Let [tex]\mu[/tex] = mean reaction time after alcohol use.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\geq[/tex] 281      {means that the reaction time is increased or remains same by frequent alcohol use}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 281      {means that the reaction time is decreased by frequent alcohol use}

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

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

where, [tex]\bar X[/tex] = sample mean reaction time (in ms) = 283

            [tex]\sigma[/tex] = population standard deviation = 28

            n = sample of alcoholics = 164

So, test statistics  =  [tex]\frac{283-281}{\frac{28}{\sqrt{164}}}[/tex]  

                              =  0.915

The value of z test statistics is 0.915.

Now, at 0.01 significance level the z table gives critical value of -2.3263 for left-tailed test. Since our test statistics is more than the critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the reaction time is increased or remains same by frequent alcohol use.

Answer:

19

Step-by-step explanation:

plug in 5 for x so f(5)=4(5)-1 = 20-1 = 19

The solution of expression f (x) = 4x - 1at x = 5 would be 19.

Given that the expression is,

f (x) = 4x - 1

Used the concept of substitution method to solve the expression.

Now, substitute x = 5 in the expression,

f (x) = 4x - 1

f (5) = 4(5) - 1

f (5) = 20 - 1

f (5) = 19

Therefore, the value of the expression is f (5) = 19.

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Answer:

The 99% confidence interval for the true mean amount of time Americans spend social networking each day is (3.02 hours, 3.36 hours).

Step-by-step explanation:

The (1 - α)% confidence interval for population mean when the population standard deviation is not known is:

[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\times \frac{s}{\sqrt{n}}[/tex]

The information provided is:

[tex]n=24\\\bar x=3.19\ \text{hours}\\s=0.2903\ \text{hours}[/tex]

Confidence level = 99%.

Compute the critical value of t for 99% confidence interval and (n - 1) degrees of freedom as follows:

[tex]t_{\alpha/2, (n-1)}=t_{0.01/2, (24-1)}=t_{0.005, 23}=2.807[/tex]

*Use a t-table.

Compute the 99% confidence interval for the true mean amount of time Americans spend social networking each day as follows:

[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\times \frac{s}{\sqrt{n}}[/tex]

     [tex]=3.19\pm 2.807\times \frac{0.2903}{\sqrt{24}}\\\\=3.19\pm 0.1663\\\\=(3.0237, 3.3563)\\\\\approx (3.02, 3.36)[/tex]

Thus, the 99% confidence interval for the true mean amount of time Americans spend social networking each day is (3.02 hours, 3.36 hours).

Answer:

3.14 miles but that doesn't sound right

Step-by-step explanation:

Assuming you have to find area of the circle its

A = πr² Radius is half of diameter so half of 2 = 1

A = 3.14 x 1²

A = 3.14 x 1

A = 3.14

If you have to find area than its 3.14 it just sounds odd

Sorry if its wrong

Answer:

.18 % increase

Step-by-step explanation:

First you would find what the difference is between the school enrollment

you would do 1456 - 1234 =  222

Then you would divide 1234/1456 = 84.75% to see the total percentage

The increase however has a percentage of .18%

To check your work you would do .18 x 1234 = 222.12 ( round to the nearest whole number so it would just be 222) then add 1234+ 222 = 1456!

Answer:

A) (1,456-1,234) ÷ 1,456

Answer:an isosceles triangle cannot be an equilateral triangle

Step-by-step explanation:

An isosceles triangle cannot be an equilateral triangle

Final answer:

An isosceles triangle has at least 2 equal sides and an equilateral triangle has all sides equal. All equilateral triangles are isosceles triangles, but not all isosceles triangles are equilateral triangles.

Explanation:

An isosceles triangle has at least 2 equal sides, while an equilateral triangle has all sides equal. Therefore, the sentence 'All isosceles triangles are equilateral triangles' is not true because not all isosceles triangles have all sides equal. On the other hand, the sentence 'All equilateral triangles are isosceles triangles' is true because every equilateral triangle automatically has at least 2 equal sides. Furthermore, it is possible for an equilateral triangle to not be an isosceles triangle if all three sides are not equal in length. So, the sentence 'An isosceles triangle cannot be an equilateral triangle' is not true.

0.07 or 7 hundredths.

Answer:

The answer is B

Step-by-step explanation:

Just did the assignment on Egn.

Answer:

465

Step-by-step explanation:

424+41=465

Question:

A small tie shop finds that at a sales level of x ties per day its marginal profit is MP(x )dollars per​ tie, where

MP(x) =1.85 + 0.12x - 0.0024x². ​Also, the shop will lose ​$65 per day at a sales level of x= 0. Find the profit from operating the shop at a sales level of x ties per day.

Answer:

P(x) = 1.85x + 0.06x^2 - 0.0008x^3 - 65

Step-by-step explanation:

MP(x) = 1.85 + 0.12(x) - 0.0024(x^2)

At sales level, x=0, loss = $65

P(0) = - $65

Integrating MP(x) with respect to x

P(x) = ∫MP(x) dx = ∫ 1.85 + 0.12(x) - 0.0024(x^2)

P(x) = 1.85x + 0.06x^2 - 0.0008x^3 + C

Therefore :

P(x) = 1.85x + 0.06x^2 - 0.0008x^3 - 65

Correct question:

A small tie shop finds that at a sales level of x ties per day its marginal profit is MP(x )dollars per​ tie, where

MP(x) =1.85 + 0.12x - 0.0024x². ​Also, the shop will lose ​$65 per day at a sales level of x= 0. Find the profit from operating the shop at a sales level of x ties per day.

Answer:

P(x) =1.85x +0.06x² - 0.0008x³ - 65

Step-by-step explanation:

Given the marginal profit function:

MP(x) =1.85 +0.12x - 0.0024x², P(0)= -65

We are to find P(x).

P(x) = ∫MP(x) dx

P(x) = ∫(1.85 + 0.12x - 0.0024x²) dx

= ∫1.85 dx+∫0.12x dx+∫(-0.0024x²)dx + C

= 1.85x + 0.06x² - 0.0008x³ + C

Initial condition at P(0) = - 65

where x(0), P(x) = -65

we have:

-65 = 1.85(0)+0.06(0)² - 0.0008x(0)³ + C

-65 = 0 + 0 - 0 + C

-65 = C

C = -65

P(x) =1.85x + 0.06x² - 0.0008x³ - 65

Answer:

The slope of the line is 2.2 or 11/5

Step-by-step explanation:

I graphed the points on the graph below and found the slope of the line.

The slope of the line is 11/ 5.

The slope is equal to the change in y over the change in x, or rise over run.

m = change in y/change in x

The change in x is equal to the difference in x-coordinates (also called run), and the change in y is equal to the difference in y-coordinates (also called rise).

m = (y₂−y₁)/(x₂−x₁)

Substituting the values of x and y into the equation to find the slope.

m = (5 − ( − 6 ))/(−4−(−9))

m =11/5

Therefore, the Slope of the line is 11/ 5.

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Answer:

Was the answer possibly C)  4,671 sq.cm. ?


Explanation:
Since the expert didn't get it right from what I'm seeing.

The surface area of the triangular prism container needed to enclose a rolled document with a diameter of 10 cm and a length of 85 cm is approximately 2637 square centimeters.

To calculate the surface area of the triangular prism container needed to enclose a rolled document with a diameter of 10 cm and a length of 85 cm, we follow these steps:

1. Determine the dimensions of the equilateral triangle base:
   - The diameter of the cylinder (10 cm) is equal to the side length of the equilateral triangle base.

2. Calculate the height of the equilateral triangle:
   - The height \( h \) of an equilateral triangle with side length \( a \) is given by:
     [tex]\[ h = \frac{\sqrt{3}}{2} a \] For \( a = 10 \) cm: \[ h = \frac{\sqrt{3}}{2} \times 10 \approx 8.66 \text{ cm} \][/tex]

3. Calculate the area of the equilateral triangle base:
   - The area \( A \) of an equilateral triangle with side length \( a \) is given by:
     [tex]\[ A = \frac{\sqrt{3}}{4} a^2 \] - For \( a = 10 \) cm: \[ A = \frac{\sqrt{3}}{4} \times 10^2 \approx 43.30 \text{ cm}^2 \][/tex]

4. Calculate the lateral surface area of the prism:
   - The lateral surface area is given by the perimeter of the triangular base times the length of the prism.
   - The perimeter \( P \) of an equilateral triangle with side length \( a \) is:
     [tex]\[ P = 3a \] For \( a = 10 \) cm: \[ P = 3 \times 10 = 30 \text{ cm} \][/tex]
   - The length of the prism is 85 cm.
   - The lateral surface area \( L \) is:
     [tex]\[ L = P \times \text{length} = 30 \times 85 = 2550 \text{ cm}^2 \][/tex]

5. Calculate the total surface area of the prism:
   - The total surface area \( S \) includes the lateral surface area and the area of the two triangular bases.
   - Total surface area \( S \) is given by:
     [tex]\[ S = L + 2 \times A \] - Substitute the values: \[ S = 2550 + 2 \times 43.30 = 2550 + 86.60 = 2636.60 \text{ cm}^2 \][/tex]

6. Round the total surface area to the nearest square centimeter:
[tex]\( S \approx 2637 \text{ cm}^2 \)[/tex]

So, the surface area of the triangular prism container needed to enclose a rolled document with a diameter of 10 cm and a length of 85 cm is approximately 2637 square centimeters.

Answer:

(1, 1), (2.4), (0.5) (470)

Step-by-step explanation:

Honestly, I only know it's this one because the first one is a linear function. If you think about it on a graph, all of the points on the first one can connect with a straight line.

Answer:

what do you need answered?

Step-by-step explanation:

Answer:

2/5

Step-by-step explanation:

khan academy

Answer:

  68.44%

Step-by-step explanation:

You compute the average the way you compute any average: add up the numbers and divide by their number.

Multiplication is a useful way to shorten the effort of repeated addition.

  (64% × 3 + 58% × 7 + 88% × 3 +33% + 100% × 2)/(3 +7 +3 + 1 + 2)

  = 1095%/16 = 68.4375%

  ≈ 68.44% . . . the average mark for the class

To find the length of the band holding four pencils together, calculate the circumference of each pencil using the formula C = 2πr, where C is the circumference and r is the radius. Multiply the circumference of each pencil by 4 to find the total length of the band.

To find the length of the band holding four pencils together, you need to calculate the circumference of the pencils. The diameter of each pencil is given as 10 mm, so the radius is half of the diameter, which is 5 mm. The formula for calculating the circumference of a circle is C = 2πr, where C is the circumference, π is a constant approximately equal to 3.14159, and r is the radius. Therefore, the circumference of each pencil is 2π(5 mm) = 10π mm. Since there are four pencils, the total length of the band is 10π mm x 4 = 40π mm. This is your answer in terms of π.

1/4

Step-by-step explanation:

1/4 is the original fraction of 3/12 simplified

Final answer:

The probability of the spinner landing on an orange section is 1/4 or 0.25, meaning there is a 25% chance it will land on orange.

Explanation:

The question involves calculating the probability of a spinner landing on a specific color. If a spinner has 12 equal-sized sections and three of them are orange, to find the probability of landing on orange, we use the ratio of the number of orange sections to the total number of sections. In this case, there are 3 orange sections and 12 sections in total, so the probability (P) is:

P(orange) = Number of orange sections / Total number of sections

P(orange) = 3 / 12

P(orange) = 1 / 4

Therefore, the probability that the spinner will land on orange is 1/4 or 0.25, which means there's a 25% chance the spinner will land on an orange section.

Answer:-2048

Step-by-step explanation:

First term(a)=1

Common ratio(r)=-2/1 or 4/-2

Common ratio(r)=-2

nth term=a x r^(n-1)

12th term=1 x (-2)^(12-1)

12th term=1 x (-2)^11

12th term=(-2)^11

12th term=-2048

The 12th term of the geometric sequence 1, −2, 4, .... is equal to -2048.

In Mathematics and Geometry, the nth term of any geometric sequence can be determined by using the following formula:

[tex]a_n=a_1(r)^{n-1}[/tex]

Where:

In this context, the common ratio would be determined as follows;

Common ratio, r = a₂/a₁

Common ratio, r = -2/1

Common ratio, r = -2

Now, we can determine the 12th term in the sequence defined by this explicit rule;

[tex]a_n=a_1(r)^{n-1}\\\\a_{12}=1(-2)^{12-1}\\\\a_{12}=(-2)^{-11}\\\\a_{12}=-2048[/tex]

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Answer:

c. 139

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

How large a sample should be taken to estimate the average age of out-of-state guests with a margin of error no larger than 5 and with a 95% level of confidence?

We need a sample size of n.

n is found when [tex]M = 5, \sigma = 30[/tex]

So

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

[tex]5 = 1.96*\frac{30}{\sqrt{n}}[/tex]

[tex]5\sqrt{n} = 1.96*30[/tex]

Simplifying by 5

[tex]\sqrt{n} = 1.96*6[/tex]

[tex](\sqrt{n})^{2} = (1.96*6)^{2}[/tex]

[tex]n = 138.30[/tex]

We round up,

So the correct answer is:

c. 139

Answer:

[tex]n=(\frac{1.960(30)}{5})^2 =138.30 \approx 139[/tex]

And if we round up to the nearest integer we got n =139, and the best answer for this case is:

c. 139

Step-by-step explanation:

For this case we have this previous info:

[tex]\sigma = 30[/tex] represent the previous estimation for the population deviation

[tex]Confidence =0.95[/tex] represent the confidence level

The margin of error for the true mean is given by this formula:

[tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]    (a)

The desired margin of error is ME =5 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex]   (b)

The critical value for a 95% of confidence interval given now can be founded using the normal distribution. For this case the critical value would be given by [tex]z_{\alpha/2}=1.960[/tex], replacing into formula (b) we got:

[tex]n=(\frac{1.960(30)}{5})^2 =138.30 \approx 139[/tex]

And if we round up to the nearest integer we got n =139, and the best answer for this case is:

c. 139