A market surveyor wishes to know how many energy drinks teenagers drink each week. They want to construct a 85% confidence interval for the mean and are assuming that the population standard deviation for the number of energy drinks consumed each week is 1.2. The study found that for a sample of 830 teenagers the mean number of energy drinks consumed per week is 7.3. Construct the desired confidence interval. Round your answers to one decimal place.

Answer:

7

Step-by-step explanation:

24/4=6.  7>6

The 12 inch cake needs 3 cups of flour.

In order to solve a problem for two different values of a quantity, its unit value is first derived. This method is known as unitary method.

Given that,

The amount of cup of flour for 8 inch cake is 2 cups.

The  given problem can be solved using unitary method as follows,

The 8 inch cake needs 2 cups.

Then, 1 inch cake needs 2/8 = 1/4 cups.

Thus, 12 inch cup requires 1/4 × 12 = 3 cups.

Hence, the number of cups needed for 12 inch cake is 3.

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Answer:

10 dimes.

Step-by-step explanation:

Let n represent number of nickels, d represent number of dimes and q represent number of quarters.

We have been given that there are 57 coins in all. We can represent this information in an equation as:

[tex]n+d+q=57...(1)[/tex]        

We are also told that the value of all coins is $4.55. We can represent this information in an equation as:

[tex]0.05n+0.10d+0.25q=4.55...(2)[/tex]

The number of nickels is 7 short of being three times the sum of the number of dimes and quarters together. We can represent this information in an equation as:

[tex]n+7=3(d+q)...(3)[/tex]

From equation (1), we will get:

[tex]d+q=57-n[/tex]

Substituting this value in equation (3), we will get:

[tex]n+7=3(57-n)[/tex]

[tex]n+7=171-3n[/tex]

[tex]n+3n+7-7=171-7-3n+3n[/tex]

[tex]4n=164[/tex]

[tex]\frac{4n}{4}=\frac{164}{4}[/tex]

[tex]n=41[/tex]

Therefore, there are 41 nickels in the bank.

[tex]d+q=57-n...(1)[/tex]  

[tex]d+q=57-41...(1)[/tex]

[tex]d+q=16...(1)[/tex]

[tex]q=16-d...(1)[/tex]

Upon substituting equation (1) and value of n in equation (2), we will get:

[tex]0.05(41)+0.10d+0.25(16-d)=4.55[/tex]

[tex]2.05+0.10d+4-0.25d=4.55[/tex]

[tex]6.05-0.15d=4.55[/tex]

[tex]6.05-6.05-0.15d=4.55-6.05[/tex]

[tex]-0.15d=-1.5[/tex]

[tex]\frac{-0.15d}{-0.15}=\frac{-1.5}{-0.15}[/tex]

[tex]d=10[/tex]

Therefore, there are 10 dimes in the bank.

Answer:

The standard deviation of the scores on a recent exam is 6.

The sample size required is 25.

Step-by-step explanation:

Let X = scores of students on a recent exam.

It is provided that the random variable X is normally distributed.

According to the Empirical rule, 99.7% of the normal distribution is contained in the range, μ ± 3σ.

That is, P (μ - 3σ < X < μ + 3σ) = 0.997.

It is provided that the scores on a recent exam were normally distributed with a range from 51 to 87.

This implies that:

P (51 < X < 87) = 0.997

So,

μ - 3σ = 51...(i)

μ + 3σ = 87...(ii)

Subtract (i) and (ii) to compute the value of σ as follows:

  μ -     3σ =    51

(-)μ + (-)3σ = (-)87

______________

-6σ = -36

σ = 6

Thus, the standard deviation of the scores on a recent exam is 6.

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

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

The margin of error of this interval is:

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

Given:

MOE = 2

σ = 6

Confidence level = 90%

Compute the z-score for 90% confidence level as follows:

[tex]z_{\alpha/2}=z_{0.10/2}=z_{0.05}=1.645[/tex]

*Use a z-table.

Compute the sample required as follows:

[tex]MOE = z_{\alpha/2}\frac{\sigma}{\sqrt{n}}\\2=1.645\times \frac{6}{\sqrt{n}}\\n=(\frac{1.645\times 6}{2})^{2}\\n=24.354225\\n\approx 25[/tex]

Thus, the sample size required is 25.

The Empirical Rule guides estimating sample sizes with specific confidence levels and margins of error.

The Empirical Rule states that about 95 percent of the values lie within two standard deviations of the mean in a normal distribution.

To estimate the sample size needed to estimate the true mean score with 90 percent confidence and an error of ±2, we can use the formula for the margin of error.

By rearranging this formula and plugging in the required values, we can determine the sample size needed to achieve the desired confidence level and margin of error.

Answer:

See answer below

Step-by-step explanation:

Hi there,

The formula above is not in point-slope form, which is of the form:

[tex]y = mx +b[/tex]

So, just simply put it in point-slope form by:

1. distributing the 1/3 term into the parentheses

[tex]y-4=\frac{1}{3}x -\frac{5}{3}[/tex]

2. add 4 to the right side of the equation to isolate y

[tex]y = \frac{1}{3} x-\frac{5}{3} +4 \\ = \frac{1}{3} x-\frac{5}{3}+\frac{12}{3} =\frac{1}{3} x+\frac{7}{3} \\ y =\frac{1}{3} x+\frac{7}{3}[/tex]

Adding 4 as 12/3 with common denominator, the resulting equation is now in point-slope form.

The "point" refers to y-intercept, which is 7/3, while the slope is the coefficient of x, which is 1/3.

thanks,

The point is (5, 4) and the slope is 1/3 in the given equation. The point-slope form of a linear equation is y - y1 = m(x - x1).

The point-slope form of a linear equation is y - y1 = m(x - x1).

Given the equation y - 4 = 1/3(x - 5), the point is (5, 4) and the slope is 1/3.

Therefore, the point is (5, 4) and the slope is 1/3.

Answer:

The matched pair t-interval for a population mean difference.

Step-by-step explanation:

The matched pair design (Used in the paired t-test or paired-samples t-test) compares the two means associated groups to conclude if there is a statistically significant difference amid these two means.

A (1 - α)% confidence interval for matched pair design can be used to determine whether there is any difference between the two groups of data.

We use the paired t-interval if we have two measurements on the same item, person or thing. We should also use this interval if we have two items that are being measured with a unique condition.

For instance, an experimenter tests the effect of a medicine on a group of patients before and after giving the doses.  

In this case a study was conducted to determine the effectiveness of a certain adult reading program.

The selected adults will be given a pretest before beginning the program and a post-test after completing the program. Then the difference between the two scores would be computed for each adult.

This is an example of matched pair design.

To analyze this data, i.e. to determine whether the program is effective or not, compute the matched pair t-interval for a population mean difference.

The subject of the question is Statistics, which pertains to a before-and-after study design. It involves the use of a pretest and posttest to evaluate the effectiveness of an adult reading program. Proper random sample selection is key to avoid bias and increase study validity.

The study mentioned in the question is under the subject of Statistics, particularly pertaining to Study Design and Data Analysis. This type of observational study is known as a before-and-after study or time series. It involves recording observations on variables of interest over a period of time before and after a treatment or intervention.

In this scenario, the intervention is the adult reading program. The observations are done in the form of a pretest (before the intervention) and a posttest (after the intervention). The difference between the results of the posttest and pretest is then calculated to determine if there has been an improvement, and if so, how significant that improvement is.

Such study designs have seen ample usage in education, health sciences, and various other fields. It's important to highlight that in this study design, it's critical to have a well-defined random sample to avoid selection bias and increase the generalizability of the study findings.

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Answer:

3/46

Step-by-step explanation:

The expected value of the amount you would win from this game is $0.85 and the variance of the amount you win is $0.06.

To calculate the expected value, we need to multiply each outcome with its probability and sum them up. The outcomes and corresponding probabilities are as follows:

Then, the expected value is (8/9)*$1.10 + (1/9)*(-$1.00) = $0.96 - $0.11 = $0.85. So, (a) expected value of the amount you win is $0.85.

To calculate the variance, we need to subtract the expected value from each outcome, square the result, multiply by the probability of each outcome and sum it all up. Variance = (8/9)*($1.10-$0.85)^2 + (1/9)*(-$1.00-$0.85)^2 = $0.06. So, (b) the variance of the amount you win is $0.06.

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The expected value of the amount you win is approximately -$0.0667 and the variance of the amount you win is approximately $1.0888.

(a) To calculate the expected value of the amount you win, we first need to determine the probability of each outcome:

1. Probability of drawing two red marbles: [tex]\( P(\text{red-red}) = \frac{5}{10} \times \frac{4}{9} = \frac{20}{90} = \frac{2}{9} \)[/tex]

2. Probability of drawing two blue marbles: [tex]\( P(\text{blue-blue}) = \frac{5}{10} \times \frac{4}{9} = \frac{20}{90} = \frac{2}{9} \)[/tex]

3. Probability of drawing one red marble and one blue marble: [tex]\( P(\text{red-blue}) = 2 \times \frac{5}{10} \times \frac{5}{9} = \frac{50}{90} = \frac{5}{9} \)[/tex]

Now, let's calculate the expected value (\( E \)):

[tex]\[ E = (P(\text{red-red}) \times \$1.10) + (P(\text{blue-blue}) \times \$1.10) + (P(\text{red-blue}) \times -\$1.00) \]\[ E = \left(\frac{2}{9} \times \$1.10\right) + \left(\frac{2}{9} \times \$1.10\right) + \left(\frac{5}{9} \times -\$1.00\right) \]\[ E = \left(\frac{4}{9} \times \$1.10\right) + \left(\frac{5}{9} \times -\$1.00\right) \]\[ E = \$\left(\frac{4}{9} \times 1.10\right) + \$\left(\frac{5}{9} \times -1.00\right) \][/tex]

[tex]\[ E = \$\left(\frac{4.40}{9} - \frac{5.00}{9}\right) \]\[ E = \$\frac{-0.60}{9} \]\[ E = -\$0.0667 \][/tex]

So, the expected value of the amount you win is approximately -$0.0667.

(b) To calculate the variance of the amount you win, we'll use the formula for variance:

[tex]\[ \text{Var}(X) = E(X^2) - (E(X))^2 \][/tex]

We already know  E(X) from part (a). Now, let's calculate E(X)²:

[tex]\[ E(X^2) = (P(\text{red-red}) \times (\$1.10)^2) + (P(\text{blue-blue}) \times (\$1.10)^2) + (P(\text{red-blue}) \times (-\$1.00)^2) \]\[ E(X^2) = \left(\frac{2}{9} \times (\$1.10)^2\right) + \left(\frac{2}{9} \times (\$1.10)^2\right) + \left(\frac{5}{9} \times (-\$1.00)^2\right) \]\[ E(X^2) = \left(\frac{4}{9} \times (\$1.21)\right) + \left(\frac{5}{9} \times \$1.00\right) \]\[ E(X^2) = \$\left(\frac{4 \times 1.21}{9} + \frac{5}{9}\right) \][/tex]

[tex]\[ E(X^2) = \$\left(\frac{4.84}{9} + \frac{5}{9}\right) \]\[ E(X^2) = \$\frac{9.84}{9} \]\[ E(X^2) = \$1.0933 \][/tex]

Now, we can calculate the variance:

[tex]\[ \text{Var}(X) = E(X^2) - (E(X))^2 \]\[ \text{Var}(X) = \$1.0933 - (-\$0.0667)^2 \]\[ \text{Var}(X) = \$1.0933 - \$0.0045 \]\[ \text{Var}(X) = \$1.0888 \][/tex]

So, the variance of the amount you win is approximately $1.0888.

Therefore, the solution is (a) Expected value: -$0.0667 and (b) Variance: $1.0888

Answer:

Check the explanation

Step-by-step explanation:

The details of the given samples are as follows:

Low dose. Number numbers of rats 20

The standard deviation . [tex]S_1[/tex]=54g

Control:

Number of rats [tex]N_2[/tex]=23

The standard deviation [tex]S_1[/tex]=32g  

[tex]H_0[/tex]: there is no more variability in low — dose weight gains than in the control weight gins  

[tex]H_1[/tex]: There is mere In-viability in low — dose weight gains than in control weight gains  

>4 The level of significance.

a= 0.05 The test statistic to test the above hypothesis is Larger variance Smaller variance  

The critical value of F (19.22) dr and at 0.05

significance level is 2.0837

The P-Value is 0.01 The test significance value is greater the the critical level is 20837.

Also. the 8-value is less then the significance level Hence, we reject the null hypothesis.

Therefore, we conclude that there is sufficient evidence to conclude that there is more variability in low — dose weight gains than in control weight gains .

Answer:

  no

Step-by-step explanation:

The angle in the polar form of a complex number can have any multiple of 2π radians added to it, and the number will be the same number. That is, there are an infinite number of representations of a complex number in polar form.

Final answer:

The polar form of a complex number is not unique due to the angle component, which can vary by multiples of full rotations (2π). However, when considering the principal value of the angle, the polar form becomes unique.

Explanation:

The polar form of a complex number is not entirely unique, the reason being that the angle (θ) in the polar form can be expressed as θ + 2πk, where k is any integer.

This is because complex numbers are represented in the complex plane, which is similar to a circle, where angles that differ by full rotations (2π radians) represent the same point.

However, the magnitude (or modulus) and the principal value of the angle (typically between -π and π) combine to give a unique representation of a complex number in polar form.

The probability that the sample mean hardness for a random sample of 12 pins is at least 51 is approximately 0.0228.

To determine the probability, we can use the central limit theorem. Since the distribution of the Rockwell hardness is normal, the distribution of the sample mean will also be normal. The formula for calculating the standard deviation of the sample mean (standard error) is given by the population standard deviation divided by the square root of the sample size. In this case, the standard error is calculated as 1.3 / sqrt(12), which is approximately 0.3746.

To find the z-score, we use the formula: z =[tex](X - μ) / σ[/tex], where X is the desired value (51), μ is the mean (50), and σ is the standard error (0.3746). Plugging in these values, we get a z-score of approximately 2.6744.

Using a standard normal distribution table, we find the probability that a z-score is greater than 2.6744 is approximately 0.0057. However, since we are interested in the probability that the sample mean hardness is at least 51, we need to consider the tail of the distribution on both sides. Therefore, the final probability is[tex]2 * 0.0057[/tex] = 0.0114.

To round the answer to four decimal places, the final probability is approximately 0.0228.

Probability that the sample mean hardness for 12 pins is at least 51 is approximately 0.0038.

To solve this problem, we'll use the Central Limit Theorem (CLT) and the properties of the normal distribution.

Given:

- Population mean[tex](\( \mu \))[/tex] = 50

- Population standard deviation [tex](\( \sigma \))[/tex] = 1.3

- Sample size (( n )) = 12

- Desired sample mean[tex](\( \bar{x} \)) = 51[/tex]

The CLT states that the distribution of sample means approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution.

For a sample size of 12, we can use the following formula to calculate the standard error[tex](\( \text{SE} \))[/tex]:

[tex]\[ \text{SE} = \frac{\sigma}{\sqrt{n}} \][/tex]

Substitute the given values:

[tex]\[ \text{SE} = \frac{1.3}{\sqrt{12}} \][/tex]

[tex]\[ \text{SE} \approx \frac{1.3}{3.4641} \][/tex]

[tex]\[ \text{SE} \approx 0.3749 \][/tex]

Now, we need to find the z-score for the sample mean of 51 using the standard normal distribution formula:

[tex]\[ z = \frac{\bar{x} - \mu}{\text{SE}} \][/tex]

Substitute the given values:

[tex]\[ z = \frac{51 - 50}{0.3749} \][/tex]

[tex]\[ z = \frac{1}{0.3749} \][/tex]

[tex]\[ z \approx 2.6679 \][/tex]

Now, we look up the probability corresponding to this z-score in the standard normal distribution table.

The probability that the sample mean hardness for a random sample of 12 pins is at least 51 is the area under the standard normal curve to the right of ( z = 2.6679 ).

Consulting a standard normal distribution table or using statistical software, we find:

[ P(Z > 2.6679) ]

This probability represents the area to the right of ( z = 2.6679 ).

Now, if we're using a standard normal distribution table, we might find the value closest to 2.67 or 2.67 itself, then look up the corresponding probability.

This probability gives us the likelihood that the sample mean hardness for a random sample of 12 pins is at least 51.

This answer involves time series analysis concepts, specifically focusing on three-week moving averages and exponential smoothing methods. It explains the results obtained from both methods for predicting week 7's forecast, comparing them using the Mean Squared Error (MSE). It suggests that the three-week moving average provides a better prediction due to a lower MSE.

The question asked is a problem in time series analysis, a category of statistics that involves the use and interpretation of data points ordered in time. The method used to analyze this data includes calculating a three-week moving average, computing mean squared error (MSE), and conducting exponential smoothing.

In the scenario given, a three-week moving average tracks an average of data over the past three weeks. It showed a forecast for week 7 as 13.33 with an MSE value of 7.74. In contrast, the exponential smoothing method, which uses a weight assigned to historic data (referred to as alpha, =0.2 in this case) forecasted a higher value of 14.76 with a slightly greater MSE of 8.17.

Between the two methods, the three-week moving average forecast provided a better model due to its lower MSE, indicating a smaller average squared distance between predicted and actual values. Although the calculations for the best value are not included here, a lower MSE (compared to =0.2) was obtained with the value =0.157. This example showcases how using different methods and changing parameters within methods can provide different forecasting results in time series analysis.

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Answer: 3 packets

12/2 = 6 seeds per packets

18/6 = 3 packets

Answer:

3

Step-by-step explanation:

If Jeanette grew 12 flowers with 2 seeds packets, that means that each seed packet grows 6 flower. 12/2=6

If each seed packet grows 6 flowers, 3 seed packets will give 18 flowers. Hope this helps!

Answer:

Check the explanation

Step-by-step explanation:

Here we have to first of all carry out dependent sample t test. consequently wore goggles first was selected at random for the reason that the reaction time in an emergency taken with goggles would be greater than the amount of reaction time in an emergency taken with not so weakened vision. So that we will get the positive differences d = impaired - normal

b)

To find 95% confidence interval first we need to find sample mean and sample sd for difference d = impaired minus normal.

We can find it using excel that is in the first attached image below,

Therefore sample mean [tex]( \bar{X}_{d} )[/tex] = 0.98

Sample sd [tex]( \bar{S}_{d} )[/tex] = 0.3788

To find 95% Confidence interval we can use TI-84 calculator,

Press STAT ----> Scroll to TESTS ---- > Scroll down to 8: T Interval and hit enter.

Kindly check the attached image below.

Therefore we are 95% confident that mean difference in braking time with impaired vision and normal vision is between ( 0.6888 , 1.2712)

Conclusion : As both values in the interval are greater than 0 , mean difference impaired minus normal is not equal to 0

There is significant evidence that  there is a difference in braking time with impaired vision and normal vision at 95% confidence level .

Bringing a DUI simulator to a high school is a good idea as it controls for any "learning" that may occur. The 95% confidence interval shows that there is a difference in braking time with impaired vision and normal vision.

In designing the experiment, bringing a DUI simulator to a high school is a good idea because it controls for any "learning" that may occur in using the simulator. It allows the students to experience the effects of impaired vision due to alcohol and measure their reaction times under both normal and impaired conditions.

To test if there is a difference in braking time with impaired vision and normal vision, a 95% confidence interval is used. The 95% confidence interval is calculated by determining the mean difference in braking time and finding the range within which the true mean difference lies.

The 95% confidence interval for the difference in braking time with impaired vision and normal vision is (0.254, 1.088) seconds. Based on this interval, there is sufficient evidence to conclude that there is a difference in braking time with impaired vision and normal vision.

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Answer:

  D. The axis of symmetry is the y-axis.

Step-by-step explanation:

The vertex is at coordinates (0, 3). Since this parabola opens vertically, its axis of symmetry is the x=coordinate of the vertex: x = 0. That is the equation of the y-axis.

The axis of symmetry is the y-axis.

Answer:

N/A

Step-by-step explanation:

what is line l?

Answer:

d. 0.0948 ± 4.032(0.0279)

Step-by-step explanation:

A 99% confidence interval for the coefficient of promotional expenditures is, First, compute the t critical value then find confidence interval.

The t critical value for the 99% confidence interval is,  

The sample size is small and two-tailed test. Look in the column headed es = 0.01 and the row headed in the t distribution table by using degree of freedom is here

for (n-2=5) degree of freedom and 99% confidence ; critical t =4.032

therefore 99% confidence interval for the slope =estimated slope -/+ t*Std error

= 0.094781123 -/+ 4.032* 0.027926367 = -0.017822 to 0.207384

Answer:

Hence the expected value for the contractor for sales is 15,300 $.

Step-by-step explanation:

Given:

Winning $27000 is 0.7 and losing 12000 $ of it about 0.3

To find :

Expected value for the contractor for sales.

Solution:

Th expected value is the average occurred  of the event.

{Suppose

a series of number like 10,30,30,30,30,60,78.

for this  expected value will be

(10+30+30+30+30+60+78+78) / 8

=10(1/8)+30(4/8)+60(1/8)+78(2/8).

78 ,10 ,30 and 60 are just like cost and 1/8 ,4/8,2/8 are probabilities of respective cost.

}

Similar for given values

Expected value with probability is =

Winning probability *cost of winning +(-losing probability * losing cost)

losing means negative impact on value so it is negative

=27000*0.7-12000*0.3

=18900-3600.

=15300 $.

The Minitab output from the t-test signifies that there is no statistically significant difference in the distances traveled by men and women at UF to get to class. The t-value and p-value obtained don't give enough evidence to reject the null hypothesis. The degrees of freedom (DF) indicate the number of independent observations in the sample.

The output from Minitab that you've shared is the result of a paired t-test comparing the mean distances traveled by men and women to get to class at UF. The null hypothesis in this context is that there is no difference in the average distances traveled by men and women (Difference = mu (F) - mu (M)). The t-value of -1.05 and the p-value of 0.305 do not provide enough evidence to reject the null hypothesis at the conventional 0.05 level of significance. Therefore, we could interpret the output as not detecting a statistically significant difference between the mean distances men and women travel to get to class at UF.

The 'DF' or degrees of freedom, indicates the number of independent observations in your sample that are free to vary once certain constraints (like the sample mean) are calculated. In this case, DF = 21, which is the sample size (pairs of men and women) minus 1.

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Answer:

Parallelograms are shapes that have four sides with two sides that are parallel. For example, some shapes that are parallelograms are squares, rectangle, rhombus and rhomboid.  

Step-by-step explanation:

No explanation :)

Final answer:

A parallelogram is a quadrilateral with parallel and congruent opposite sides, congruent opposite angles, and diagonals that bisect each other.

Explanation:

A parallelogram is a four-sided polygon, also known as a quadrilateral, where opposite sides are parallel and equal in length. There are several properties that define a parallelogram:

An example of a parallelogram is a rectangle, which also has all angles equal to 90 degrees, making it a special type of parallelogram. Another example is a rhombus, which has all sides of equal length. The term parallelogram comes from the Greek 'parallelos' and 'gramme', meaning 'parallel lines' and 'line' respectively.

We are 90% confident that the true proportion of all Connecticut baseball fans who say their favorite team is the Yankees is between 0.511 and 0.589.

A confidence interval is a range of values that is likely to contain the true value of an unknown parameter, such as a population means or proportion, based on a sample of data from that population.

It is a statistical measure of the degree of uncertainty or precision associated with a statistical estimate.

We have,

To calculate a 90% confidence interval for the proportion of all Connecticut baseball fans who say their favorite team is the Yankees, we can use the formula:

CI = p ± z √((p(1-p))/n)

where:

p is the sample proportion (0.55)

z* is the critical z-value for a 90% confidence level (1.645)

n is the sample size (803)

Plugging in the values,

CI = 0.55 ± 1.645 √((0.55(1-0.55))/803)

CI = 0.55 ± 0.042

Therefore,

The 90% confidence interval for the proportion of all Connecticut baseball fans who say their favorite team is the Yankees is (0.508, 0.592).

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To calculate a 90% confidence interval for the proportion of Connecticut baseball fans who favor the Yankees, the standard error was computed and multiplied by the Z-score for 90% confidence. The confidence interval was found to be between 52.11% and 57.89%, meaning there is a 90% chance the true proportion falls within this range.

The question requires the calculation of a 90% confidence interval for the proportion of all Connecticut baseball fans who favor the New York Yankees. A sample proportion (p-hat) of 803 Connecticut baseball fans showed that 55% (or 0.55) favored the Yankees. To calculate the confidence interval, we use the formula for the confidence interval of a proportion:

CI = p-hat ± Z*sqrt[(p-hat)(1-p-hat)/n], where Z is the Z-score that corresponds to the level of confidence and n is the sample size. For a 90% confidence level, the Z-score is approximately 1.645.

Calculating the standard error (SE):
SE = sqrt[(0.55)(0.45)/803] = sqrt[0.2475/803] = sqrt[0.000308344] = 0.017562

Then, the margin of error (ME):
ME = Z*SE = 1.645 * 0.017562 = 0.028894

The 90% confidence interval (CI) is:
CI = 0.55 ± 0.028894
CI = [0.521106, 0.578894]

Interpreting this confidence interval, we are 90% confident that the true proportion of all Connecticut baseball fans who favor the Yankees falls between 52.11% and 57.89%.

Answer:

Probability that their mean height is less than 68 inches is 0.0764.

Step-by-step explanation:

We are given that in the united states, the height of men are normally distributed with the mean 69 inches and standard deviation 2.8 inches.

Also, 16 men are randomly selected.

Let [tex]\bar X[/tex] = sample mean height

The z-score probability distribution for sample mean is given by;

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

where, [tex]\mu[/tex] = population mean height = 69 inches

            [tex]\sigma[/tex] = population standard deviation = 2.8 inches

            n = sample of men = 16

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

So, probability that the mean height of 16 randomly selected men is less than 68 inches is given by = P([tex]\bar X[/tex] < 68 inches)

 P([tex]\bar X[/tex] < 68 inches) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{68-69}{\frac{2.8}{\sqrt{16} } }[/tex] ) = P(Z < -1.43) = 1 - P(Z [tex]\leq[/tex] 1.43)

                                                           = 1 - 0.9236 = 0.0764

Now, in the z table the P(Z  x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 1.43 in the z table which has an area of 0.92364.

Therefore, probability that their mean height is less than 68 inches is 0.0764.

Answer:

choice a.)  11m

Step-by-step explanation:

2(5m) + m  =  10m + m = 11m

Answer:

1/x^2

Step-by-step explanation:

When you have a negative sign in the exponent, the integer will become fraction.

Answer:

17.67 cm

Step-by-step explanation:

[tex]\sqrt{a^2+b^2}[/tex] = x

16^2 = 256

7.5^2 = 56.25

Add.

256 + 56.25 = 312.25

[tex]\sqrt{312.25}= 17.67[/tex]

The missing side of the triangle is x = 17.67 cm

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

|AC|^2 = |AB|^2 + |BC|^2    

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

The Pythagorean theorem formula:

a² + b² = c²

Replacing by the values we have;

16² + 7.5² = x²

x² = 256 + 56.25

x²  = 312.25

x = √312.25 cm

x = 17.67 cm

Therefore, the correct answer is x = 17.67 cm

Learn more about Pythagoras theorem here:

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The arc length formed by the 2 radio is 15.24 yards

Step-by-step explanation:

Angle between the 2 radio = 45°

Radius = 64 yards

Arc length = (45/360) (2π) (64)

= (1/8) (2π) (64

= 16π

= 16(3.14)

=15.24 yards

The arc length formed by the 2 radio is 15.24 yards

Complete Question:

From a point along a straight road, the angle of elevation to the top of a hill is 33° . A distance of 200 ft farther down the road, the angle of elevation to the top of the hill is 20°. How high is the hill?

Answer:

The hill is 165.87 ft high

Step-by-step explanation:

Check the file attached below for a pictorial understanding of the question

[tex]tan \theta = \frac{opposite}{Adjacent}[/tex]

From ΔABC

[tex]tan 33 = \frac{y}{x} \\[/tex]

[tex]y = x tan 33[/tex]..........(1)

From ΔABD

[tex]tan 20 = \frac{y}{x + 200} \\[/tex]

[tex]y = (x + 200) tan 20[/tex]............(2)

Equating (1) and (2)

[tex]x tan 33 = (x+200) tan20\\xtan33 = xtan20 + 200tan20\\0.649x = 0.364x + 72.794\\0.649x - 0.364x = 72.794\\0.285x = 72.794\\x = 72.794/0.285\\x = 255.42 ft[/tex]

Substitute the value of x into equation (1)

[tex]y = 255.42 tan 33[/tex]

y = 165.87 ft

The height of the hill is 550 feet.

Given:

- [tex]\(\theta_1 = 31^\circ\)[/tex]

- [tex]\(\theta_2 = 24^\circ\)[/tex]

- [tex]\(d = 320\) feet[/tex]

We use the formula for the height of the hill \(h\):

[tex]\[h = \frac{d \tan(\theta_2) \tan(\theta_1)}{\tan(\theta_1) - \tan(\theta_2)}\][/tex]

First, we calculate [tex]\(\tan(31^\circ)\)[/tex] and  [tex]\(\tan(24^\circ)\)[/tex]:

[tex]\[\tan(31^\circ) \approx 0.6009\][/tex]

[tex]\[\tan(24^\circ) \approx 0.4452\][/tex]

Now, substitute these values into the formula:

[tex]\[h = \frac{320 \times 0.4452 \times 0.6009}{0.6009 - 0.4452}\][/tex]

Calculate the numerator:

[tex]\[320 \times 0.4452 \times 0.6009 \approx 85.676256\][/tex]

Calculate the denominator:

[tex]\[0.6009 - 0.4452 \approx 0.1557\][/tex]

Now, divide the numerator by the denominator:

[tex]\[h = \frac{85.676256}{0.1557} \approx 550.41\][/tex]

Rounding to the nearest foot, the height of the hill is:

550 feet.




Complete question is here
From a point along a straight road, the angle of elevation to the top of a hill is 31º. From 320 n farther down the road, the angle of elevation to the top of the hill is 24º. How high is the hill? Round to the nearest foot.

Answer:

The equation of the ellipse is standard form is expressed as:

x²/81 + y²/9 = 1

Step-by-step explanation:

General equation of an ellipse is expressed as shown below:

x²/a² + y²/b² = 1

Length of the major axis = 2a

Length of the Minor axis = 2b

Given length of major axis = 18

18 = 2a

a = 9

Similarly, if the length of the minor axis is 6, then

6 = 2b

b = 3

The equation of the ellipse becomes;

x²/9² + y²/3² = 1

x²/81 + y²/9 = 1

Finding the LCM

(x²+9y²)/81 = 1

x²+9y² = 81

Step-by-step explanation:

A circular swimming pool has a tacius of 28 ft. There is a path all the way around the pool that is 4 ft wide. A fence is going to be built around the outside edge of the pool path

WE need to find the circumference of the circle

radius of circular swimming pool is 28 feet

path is 4 ft wide

so we add 4 with radius

radius of the pool with path is 28+4= 32

[tex]circumference =2\pi (r)[/tex]

where r is the radius

r=32

[tex]circumference =2\pi (r)\\circumference =2\pi (32)=200.96=201[/tex]

Answer:

201 feet

Answer:

1. the probability that giraffe will be shorter than 17 feet tall is equal to 0.1056

2. the probability that a randomly selected giraffe will be between 16 and 19 feet tall is equal to 0.8882

3. the the 90th percentile for the height of giraffes is 19.024

Step-by-step explanation:

To calculate the probability that a giraffe will be shorter than 17 feet tall, we need to standardize 17 feet as:

[tex]z=\frac{x-m}{s}[/tex]

Where x is the height of the adult giraffe, m is the mean and s is the standard deviation, so 17 feet is equivalent to:

[tex]z=\frac{17-18}{0.8}=-1.25[/tex]

Now, the probability that giraffe will be shorter than 17 feet tall is equal to P(z<-1.25). Then, using the standard normal distribution table, we get that:

[tex]P(z<-1.25)=0.1056[/tex]

At the same way, 16 and 19 feet tall are equivalent to:

[tex]z=\frac{16-18}{0.8}=-2.5\\z=\frac{19-18}{0.8}=1.25[/tex]

So, the probability that a randomly selected giraffe will be between 16 and 19 feet tall is equal to:

[tex]P(-2.5<z<1.25)=P(z<1.25)-P(z<-2.5)\\P(-2.5<z<1.25)=0.8944-0.0062\\P(-2.5<z<1.25)=0.8882[/tex]

Finally, to find the the 90th percentile for the height of giraffes, we need to find the value z that satisfy:

[tex]P(Z<z)=0.9[/tex]

Now, using the standard normal distribution table we get that z is equal to 1.28. Therefore, the height x of the giraffes that is equivalent to 1.28 is:

[tex]z=\frac{x-m}{s} \\1.28=\frac{x-18}{0.8} \\x=(1.28*0.8)+18\\x=19.024[/tex]

it means that the the 90th percentile for the height of giraffes is 19.024

Using Z-scores, the probability that a randomly selected giraffe is less than 17 feet tall is approximately 0.106, the probability that it is between 16 and 19 feet tall is approximately 0.888. The 90th percentile in height for giraffes is about 19.02 feet.

These questions are related to normal distribution. The formula of normal distribution (Z-score) is Z = (X - μ)/σ, where X is the specific value, μ is the mean, and σ is the standard deviation.

For the first question, we want to find the probability that a randomly selected giraffe is less than 17 feet tall. The Z-score is calculated as Z = (17 - 18) / 0.8 = -1.25. Using the Z-table, the probability that a giraffe is less than 17 feet tall is approximately 0.106.

For the second question, we need to find the probability that a randomly selected giraffe will be between 16 and 19 feet tall. We calculate two Z-scores: Z1 = (16 - 18) / 0.8 = -2.5 and Z2 = (19 - 18) / 0.8 = 1.25. Using the Z-table, the probability that a giraffe is between 16 and 19 feet tall is approximately 0.894-0.006 = 0.888.

For the third question, we need to find the 90th percentile for the height of giraffes. It corresponds to the Z-score of 1.282 on the Z-table. Hence, X = μ + Zσ = 18 + 1.282*0.8 = 19.02 feet.

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