Suppose that a fair coin is tossed ten times. Each time it lands heads you win a dollar, and each time it lands tails you lose a dollar. Calculate the probability that your total winnings at the end of this game total two dollars, and the probability that your total winnings total negative two dollars.

Answers

Answer 1

Answer:

Both have the same probability of 0.909 or 9.09%

Step-by-step explanation:

For each coin toss, there are only two possible outcomes, heads or tails. Since order is not important in this scenario the number of heads or tails can vary from 0 to 10. Let n be the number of heads flipped in 10 tosses, the number of tails is 10-n. Therefore, the 11 possible outcomes as well as their resulting values for the bet are:

[tex]\begin{array}{ccc}Heads&Tails&Value(\$)\\0&10&-10\\1&9&-8\\2&8&-6\\3&7&-4\\4&6&-2\\5&5&0\\6&4&2\\7&3&4\\8&2&6\\9&1&8\\10&0&10\end{array}[/tex]

Looking at the values above, there is only one outcome in which total winnings are two dollars, and only one in which total winnings are negative two dollars.

Therefore, the probability for each scenario is the same and given by:

[tex]\frac{1}{11}=0.0909=9.09\%[/tex]


Related Questions

Let C be the positively oriented square with vertices (0,0), (1,0), (1,1), (0,1). Use Green's Theorem to evaluate the line integral ∫C7y2xdx+8x2ydy.

Answers

Answer:

1/2

Step-by-step explanation:

The interior of the square is the region D = { (x,y) : 0 ≤ x,y ≤1 }. We call L(x,y) = 7y²x, M(x,y) = 8x²y. Since C is positively oriented, Green Theorem states that

[tex]\int\limits_C {L(x,y)} \, dx + {M(x,y)} \, dy = \int\limits^1_0\int\limits^1_0 {(Mx - Ly)} \, dxdy[/tex]

Lets calculate the partial derivates of M and L, Mx and Ly. They can be computed by taking the derivate of the respective value, treating the other variable as a constant.

Mx(x,y) = d/dx 8x²y = 16xyLy(x,y) = d/dy 7y²x = 14xy

Thus, Mx(x,y) - Ly(x,y) = 2xy, and therefore, the line ntegral is equal to the double integral

[tex] \int\limits^1_0\int\limits^1_0 {2xy} \, dxdy[/tex]

We can compute the double integral by applying the Barrow's Rule, a primitive of 2xy under the variable x is x²y, thus the double integral can be computed as follows

[tex]\int\limits^1_0\int\limits^1_0 {2xy} \, dxdy = \int\limits^1_0 {x^2y} |^1_0 \,dy = \int\limits^1_0 {y} \, dy = \frac{y^2}{2} \, |^1_0 = 1/2[/tex]

We conclude that the line integral is 1/2

Final answer:

To evaluate the line integral using Green's Theorem, we need to find the curl of the vector field and the area enclosed by the square. The line integral of the vector field along the square is equal to the double integral of the curl over the region enclosed by the square. Using this method, we can find the value of the line integral to be 1/3.

Explanation:

To evaluate the line integral using Green's Theorem, we first need to find the curl of the vector field. In this case, the vector field is F(x, y) = 7y^2x i + 8x^2y j. Taking the partial derivatives of its components with respect to x and y, we get curl(F) = (8x^2 - 14xy^2) k.

Next, we need to find the area enclosed by the square C, which is 1 unit^2. Using Green's Theorem, the line integral of F along C is equal to the double integral of curl(F) over the region D enclosed by C. Integrating curl(F) with respect to y, we get -7xy^2 + 6x^2y. Integrating this with respect to x over the given limits, we find the value of the line integral to be 1/3.

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For each of the following scenarios state whether H0 should be rejected or not. State any assumptions that you make beyond the information that is given.
(a) H0 : µ = 4, H1 : µ 6= 4, n = 15, X = 3.4, S = 1.5, α = .05.
(b) H0 : µ = 21, H1 : µ < 21, n = 75, X = 20.12, S = 2.1, α = .10.
(c) H0 : µ = 10, H1 : µ 6= 10, n = 36, p-value = 0.061.

Answers

Answer:

a)[tex]H_0 :\mu = 4\\ H_1 : \mu \neq 4[/tex] , n = 15 , X=3.4 , S=1.5 , α = .05

Formula : [tex]t = \frac{x-\mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{3.4-4}{\frac{1.5}{\sqrt{15}}}[/tex]

[tex]t =-1.549[/tex]

p- value = 0.607(using calculator)

α = .05

p- value > α

So, we failed to reject null hypothesis

b)[tex]H_0 :\mu = 21\\ H_1 : \mu < 21[/tex] , n =75 , X=20.12 , S=2.1 , α = .10

Formula : [tex]t = \frac{x-\mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{20.12-21}{\frac{2.1}{\sqrt{75}}}[/tex]

[tex]t =-3.6290[/tex]

p- value = 0.000412(using calculator)

α = .1

p- value< α

So, we reject null hypothesis

(c) [tex]H_0 :\mu = 10\\ H_1 : \mu \neq 10[/tex], n = 36, p-value = 0.061.

Assume α = .05

p-value = 0.061.

p- value > α

So, we failed to reject null hypothesis

Final answer:

The decision to reject the null hypothesis in each scenario depends on comparing calculated test statistics (or given p-value) to critical values associated with the significance level. In (a) and (c), we may not reject H0, and in (b) we would reject H0 if our test statistic is larger than the critical value.

Explanation:

In hypothesis testing, we compare the test statistic, often a t-value, to the critical value determined by our chosen significance level, α. If the test statistic is greater, we reject the null hypothesis (H0).

(a) In the first scenario, we must calculate the test statistic: t = (X - µ) / (S/√n) = (3.4 - 4) / (1.5/√15); if this absolute value is less than our critical value associated with α = .05 and degrees of freedom = 14, we do not reject H0.

(b) For the second, the test statistic would be (20.12 - 21) / (2.1/√75); compare its value to the critical value associated with α = .10 and degrees of freedom = 74. If it is larger, we reject H0 due to the lower tail test in this scenario.

(c) In the third scenario, the p-value is given. Since our p-value = 0.061 is larger than our α = .05, we would not reject H0.

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Let X be the number of material anomalies occurring in a particular region of an aircraft gas-turbine disk. The article "Methodology for Probabilistic Life Prediction of Multiple-Anomaly Materials"� proposes a Poisson distribution for X. Suppose that ? = 4. (Round your answers to three decimal places.) (a) Compute both P(X ? 4) and P(X < 4). (b) Compute P(4 ? X ? 5). (c) Compute P(5 ? X). (d) What is the probability that the number of anomalies does not exceed the mean value by more than one standard deviation?

Answers

Answer:

0.6284,0.4335,0.1953.0.9786

Step-by-step explanation:

Given that X the number of material anomalies occurring in a particular region of an aircraft gas-turbine disk is following a poisson distribution with parameter 4

a) [tex]P(X\leq 4)=0.6284\\P(X<4)=0.4335[/tex]

b) [tex]P(4\leq x<5)\\=P(4)=0.1953\\[/tex]

c) P([tex]5\leq x)[/tex]=0.8046

d) the probability that the number of anomalies does not exceed the mean value by more than one standard deviation

=[tex]P(0\leq X\leq 8)\\=F(8)-F(0)\\=0.9786[/tex]

The average price of homes sold in the U.S. in the past year was $220,000. A random sample of 81 homes sold this year showed a sample mean price of $210,000. It is known that the standard deviation of the population is $36,000. Using a 1% level of significance, test to determine if there has been a significant decrease in the average price homes. Use the p value approach. Make sure to show all parts of the test, including hypotheses, test statistic, decision rule, decision and conclusion.

Answers

Final answer:

To test if there has been a significant decrease in the average price of homes sold in the U.S., we will conduct a hypothesis test using the p-value approach. We will define the null and alternative hypotheses, calculate the Z-test statistic, compare the p-value to the significance level, and make a conclusion based on the results.

Explanation:

To test if there has been a significant decrease in the average price of homes sold in the U.S., we will conduct a hypothesis test using the p-value approach. Let's define our hypotheses:

Null hypothesis (H0): The average price of homes sold in the U.S. is not significantly different from $220,000.

Alternative hypothesis (Ha): The average price of homes sold in the U.S. is significantly less than $220,000.

Next, we need to calculate the test statistic. Since the population standard deviation is known, we can use a Z-test. The formula for the Z-test statistic is:

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

In this case, the sample mean is $210,000, the population mean is $220,000, the population standard deviation is $36,000, and the sample size is 81. Plugging these values into the formula:

Z = (210,000 - 220,000) / (36,000 / sqrt(81))

Calculating this gives us a Z-statistic of -1.6875.

The final step is to compare the p-value of the test statistic to the significance level. Since the significance level is 1%, the critical value is 0.01. We can use a Z-table or calculator to find the p-value corresponding to a Z-statistic of -1.6875. The p-value is approximately 0.0466.

Since the p-value is less than the significance level of 0.01, we reject the null hypothesis. This means that there is sufficient evidence to conclude that there has been a significant decrease in the average price of homes sold in the U.S.

Stainless steels are frequently used in chemical plants to handle corrosive fluids, however, these steels are especially susceptible to stress corrosion cracking in certain environments. In a sample of 295 steel alloy failures that occurred in oil refineries and petrochemical plants in Japan over the last 10 tears, 118 were caused by stress corrosion cracking and corrosion fatigue (Materials Performance, 1981). Construct a 95% confidence interval for the true proportion of alloy failures caused by stress corrosion cracking.

Answers

Answer: 95% confidence interval would be (0.344,0.456).

Step-by-step explanation:

Since we have given that

n = 295

x = 118

so, [tex]\hat{p}=\dfrac{x}{n}=\dfrac{118}{295}=0.4[/tex]

At 95% confidence, z = 1.96

So, margin of error would be

[tex]z\times \sqrt{\dfrac{p(1-p)}{n}}\\\\=1.96\times \sqrt{\dfrac{0.4\times 0.6}{295}}\\\\=0.056[/tex]

so, 95% confidence interval would be

[tex]\hat{p}\pm \text{margin of error}\\\\=0.4\pm 0.056\\\\=(0.4-0.056,0.4+0.056)\\\\ =(0.344,0.456)[/tex]

Hence, 95% confidence interval would be (0.344,0.456).

Answer:

95% confidence interval would be (0.344,0.456).

Step-by-step explanation:

Complete parts ​(a) through ​(c) below. ​
(a) Determine the critical​ value(s) for a​ right-tailed test of a population mean at the alphaequals0.01 level of significance with 10 degrees of freedom. ​
(b) Determine the critical​ value(s) for a​ left-tailed test of a population mean at the alphaequals0.10 level of significance based on a sample size of nequals15. ​
(c) Determine the critical​ value(s) for a​ two-tailed test of a population mean at the alphaequals0.01 level of significance based on a sample size of nequals12.

Answers

Answer:

a) t =  2.7638

b) t = - 2.6245

c) t = 3.1058      on the right side    and

   t  = -3.1058    on the left

Step-by-step explanation:

a)Determine critical value for a right-tail test  for α = 0.01 level of significance and 10 degrees of fredom

From t-student table we find:

gl  =  10   and α = 0.01       ⇒  t =  2.7638

b)Determine   critical value for a left-tail test  for α = 0.01 level of significance  and sample size n = 15

From t-student table we find:

gl  =  14   and α = 0.01           gl  =  n - 1      gl  = 15 - 1    gl = 14

t = - 2.6245

c) Determine critical value for a two tails-test  for α = 0.01 level of  significance the  α/2   =   0.005  and sample size  n = 12

Then

gl  =  11   and α = 0.005

t = 3.1058      on the right side of the curve and by symmetry

t = - 3.1058  

From t-student table we find:

Find the absolute maximum and absolute minimum values of f on the given interval.
a) f(t)= t sqrt(36-t^2) [-1,6]
absolute max=
absolute min=
b) f(t)= 2 cos t + sin 2t [0,pi/2]
absolute max=
absolute min=

Answers

Answer:

absolute max= (4.243,18)

absolute min =(-1,-5.916)

absolute max=(pi/6, 2.598)

absolute min = (pi/2,0)

Step-by-step explanation:

a) [tex]f(t) = t\sqrt{36-t^2} \\[/tex]

To find max and minima in the given interval let us take log and differentiate

[tex]log f(t) = log t + 0.5 log (36-t^2)\\Y(t) = log t + 0.5 log (36-t^2)[/tex]

It is sufficient to find max or min of Y

[tex]y'(t) = \frac{1}{t} -\frac{t}{36-t^2} \\\\y'=0 gives\\36-t^2 -t^2 =0\\t^2 =18\\t = 4.243,-4.243[/tex]

In the given interval only 4.243 lies

And we find this is maximum hence maximum at  (4.243,18)

Minimum value is only when x = -1 i.e. -5.916

b) [tex]f(t) = 2cost +sin 2t\\f'(t) = -2sint +2cos2t\\f"(t) = -2cost-4sin2t\\[/tex]

Equate I derivative to 0

-2sint +1-2sin^2 t=0

sint = 1/2 only satisfies I quadrant.

So when t = pi/6 we have maximum

Minimum is absolute mini in the interval i.e. (pi/2,0)

One method for measuring air pollution is to measure the concentration of carbon monoxide, or CO, in the air. Suppose Nina, an environmental scientist, wishes to estimate the CO concentration in Budapest, Hungary. She randomly selects 48 locations throughout the city measures the CO concentration at each location. Based on her 48 samples, she computes the margin of error for a 95% t-confidence interval for the mean concentration of CO in Budapest, in g/m3, to be 4.28 What would happen to the margin of error if Nina decreases the confidence level to 90%? Nina increases the confidence level to 99%? Nina decreases the sample size to 34 locations? Nina increases the sample size to 70 locations? Answer Bank Decrease Stay the sameIncrease

Answers

Answer:

a) Nina decreases the confidence level to 90%?  (Decrease)

b) Nina decreases the sample size to 34 locations? (Increase)

c) Nina increases the sample size to 70 locations?   (Decrease)

Step-by-step explanation:

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=48 represent the original sample size  

Confidence =95% or 0.95

ME=4.28 represent the margin of error.

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)  

And the margin of error is given by the following expression:

[tex]ME= t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (4)

Based on the formula (4) we can answer all the questions involved:

a) Nina decreases the confidence level to 90%?

On this case the value for [tex]t_{\alpha/2}[/tex] will also decrease so the margin of error would decrease.

b) Nina decreases the sample size to 34 locations?

If we analyze the original sample size of 48 we see that if we reduce the value of n to 34, the margin of error would increase, because n is on the denominator of the margin of error.

c) Nina increases the sample size to 70 locations?

If we analyze the original sample size of 48 we see that if we increase the value of n to 70, the margin of error would decrease, because n is on the denominator of the margin of error.

There are 25 dogs playing in the dog park. You are a "dog" person and wonder which dog will be the first to come up to you when you enter the park. There are 15 golden retrievers, 5 pugs, 4 pomeranians, and 1 terrier. What is the probability that the first dog to come over to you will be a pug?

I chose 5/25

2. One Psyc 317 class has 10 people in it; another has 50 people in it. The average grade in the 10-person class is 72% (high probability of getting a C); the average grade in the 50-person class is 85% (high probability of getting a B). Which class average is the most reliable?

a. the 10 person class

b. 50 person class

c. cannot determine with this information

d. both equally

I chose the 50 person class.

Answers

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Final answer:

The probability of a pug approaching first in a park of 25 dogs is 5/25 or 1/5. The average grade of a larger class is typically a more reliable representation of the group's performance than that of a smaller one.

Explanation:

For the first question, the probability of a pug being the first dog to approach you in a park with 25 dogs, 5 of them being pugs, is indeed 5/25, or 1/5. This fraction represents the ratio of the desired outcome (a pug approaching you first) to the total number of possible outcomes (any of the 25 dogs in the park could potentially be the first to approach).

For the second part of the question - determining the more reliable average grade between two classes - the class with 50 students is the better choice. This conclusion is based on statistical reasoning. A larger sample size (in this case, the larger class) generally provides a more reliable average than a smaller sample size.

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A poll showed that 48 out of 120 randomly chosen graduates of California medical schools last year intended to specialize in family practice. What is the width of a 90 percent confidence interval for the proportion that plan to specialize in family practice? Select one:a. ± .0736b. ± .0447c. ± .0876d. ± .0894

Answers

Answer:

± 0.0736

Step-by-step explanation:

Data provided in the question:

randomly chosen graduates of California medical schools last year intended to specialize in family practice, p = [tex]\frac{48}{120}[/tex] = 0.4

Confidence level = 90%

sample size, n = 120

Now,

For 90% confidence level , z-value = 1.645

Width of the confidence interval = ± Margin of error

= ± [tex]z\times\sqrt\frac{p\times(1-p)}{n}[/tex]

= ± [tex]1.645\times\sqrt\frac{0.4\times(1-0.4)}{120}[/tex]

= ± 0.07356 ≈ ± 0.0736

Hence,

The correct answer is option  ± 0.0736

The correct option is a. [tex]\±0.0736.[/tex] The width of a [tex]90\%[/tex] confidence interval for the proportion that plan to specialize in family practice

To find the width of a confidence interval for a proportion, we can use the formula:

[tex]\[ \text{Width} = Z \times \sqrt{\frac{p(1-p)}{n}} \][/tex]

where:

[tex]\( Z \)[/tex] is the Z-score corresponding to the desired confidence level,

[tex]\( p \)[/tex] is the sample proportion,

[tex]\( n \)[/tex] is the sample size.

Given:

[tex]Sample\ proportion \( p = \frac{48}{120} = \frac{2}{5} = 0.4 \)[/tex],

[tex]Sample\ size \( n = 120 \)[/tex]

[tex]Confidence \ level = 90\%[/tex], which corresponds to a Z-score of approximately [tex]1.645.[/tex]

Substitute the values into the formula:

[tex]\[ \text{Width} = 1.645 \times \sqrt{\frac{0.4 \times 0.6}{120}} \][/tex]

[tex]\[ \text{Width} = 1.645 \times \sqrt{\frac{0.24}{120}} \][/tex]

[tex]\[ \text{Width} = 1.645 \times \sqrt{0.002} \][/tex]

[tex]\[ \text{Width} = 1.645 \times 0.0447 \][/tex]

[tex]\[ \text{Width} = 0.0736 \][/tex]

Suppose a basketball player is practicing shooting, and has a prob-ability .95 of making each of his shots. Also assume that his shots are in-dependent of one another. Using the Poisson distribution, approximate theprobability that there are at most 2 misses in the first 100 attempts

Answers

Answer:

0.082

Step-by-step explanation:

Number of attempts = n = 100

Since there are only two outcomes and in-dependent of each other, the probability of missing a shot  = 1 - Probability of making each shot

p = 1 - 0.95 = 0.05

Possion Ratio (λ) = np where n is the number of events and p is the probability of the shot missing

λ = 100 x 0.05 = 5

Define X such that X = Number of misses and X ≅ Poisson (λ = 5)

P [X ≤ 2] = P [X = 0] + P [X = 1] + P [X = 2]

P [X ≤ 2] = e⁻⁵ + e⁻⁵ x 5 + e⁻⁵ x 5²/2!

P [X ≤ 2] = e⁻⁵ [1 + 5 + 5²/2!]

P [X ≤ 2] = e⁻⁵ x 12.25 = 0.082

The required probability that there are at most 2 misses in the first 100 attempts is 0.082

Which function has (2,8) on its graph

Answers

Answer:

y = 2x^2

Step-by-step explanation:

The the coordinates (2,8) are expressed in terms of (x,y). Substitute the x with 2 and y with 8 and plug them into the formulas. The one that has the two sides equal to each other is the function that has (2,8) on its line.

For the given function, determine consecutive values of x between which each real zero is located. f(x) = –11x^4 – 5x^3 – 9x^2 + 12x + 10

Answers

Answer:

[-1, 0][0, 1]

Step-by-step explanation:

Descartes' rule of signs tells you this function, with its signs {- - - + +}, having one sign change, will have one positive real root.

When odd-degree terms have their signs changed, the signs {- + - - +} have three changes, so there will be 1 or 3 negative real roots.

The constant term (10) tells us the y-intercept is positive. The sum of coefficients is -11 -5 -9 +12 +10 = -3, so f(1) < 0 and there is a root between 0 and 1.

When odd-degree coefficients change sign, the sum becomes -11 +5 -9 -12+10 = -17, so there is a root between -1 and 0.

__

Synthetic division by (x+1) gives a quotient of -11x^3 +6x^2 -15x +27 -17/(x+1), which has alternating signs, indicating -1 is a lower bound on real roots.

Real roots are located in the intervals [-1, 0] and [0, 1].

_____

The remaining roots are complex. All roots are irrational.

The attached graph confirms that roots are in the intervals listed here. Newton's method iteration is used to refine these to calculator precision. Dividing them from f(x) gives a quadratic with irrational coefficients and complex roots.

A random sample of 10 shipments of stick-on labels showed the following order sizes.10,520 56,910 52,454 17,902 25,914 56,607 21,861 25,039 25,983 46,929PictureClick here for the Excel Data File(a) Construct a 95 percent confidence interval for the true mean order size. (Round your answers to the nearest whole number.) The 95 percent confidence interval to

Answers

Answer:

Confidence Interval: (21596,46428)

Step-by-step explanation:

We are given the following data set:

10520, 56910, 52454, 17902, 25914, 56607, 21861, 25039, 25983, 46929

Formula:

[tex]\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}[/tex]  

where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.  

[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]

[tex]Mean =\displaystyle\frac{340119}{10} = 34011.9[/tex]

Sum of squares of differences = 551869365.6 + 524322983.6 + 340111052.4 + 259528878 + 65575984.41 + 510538544 + 147644370.8 + 80512934.41 + 64463235.21 + 166851472.4 = 2711418821

[tex]S.D = \sqrt{\frac{2711418821}{9}} = 17357.09[/tex]

Confidence interval:

[tex]\mu \pm t_{critical}\frac{\sigma}{\sqrt{n}}[/tex]

Putting the values, we get,

[tex]t_{critical}\text{ at degree of freedom 9 and}~\alpha_{0.05} = \pm 2.2621[/tex]

[tex]34011.9 \pm 2.2621(\frac{17357.09}{\sqrt{10}} ) = 34011.9 \pm 12416.20 = (21595.7,46428.1) \approx (21596,46428)[/tex]

In simple regression analysis, if the correlation coefficient is a positive value, then Select one:

A. the slope of the regression line must also be positive.

B. the least squares regression equation could have either a positive or a negative slope.

C. the y-intercept must also be a positive value.

D. the coefficient of determination can be either positive or negative, depending on the value of the slope.

E. the standard error of estimate can have either a positive or a negative value.

Answers

Final answer:

In simple regression analysis, a positive correlation coefficient means that the slope of the regression line must also be positive, as both the dependent and independent variables increase or decrease together.

Explanation:

In simple regression analysis, the correlation coefficient's sign (positive or negative) informs us about the direction of the relationship between the two variables.

A positive correlation coefficient indicates that the variables move in the same direction: as one increases, so does the other, and as one decreases, so does the other. This characteristic of correlation directs us to the correct answer to the student's question.

Considering the options provided:

A. The slope of the regression line must also be positive. B. The least squares regression equation could have either a positive or a negative slope. C. The y-intercept must also be a positive value. D. The coefficient of determination can be either positive or negative, depending on the value of the slope. E. The standard error of estimate can have either a positive or a negative value.

The slope of the regression line is directly determined by the correlation coefficient in the context of simple linear regression. Given that the correlation coefficient is positive, the slope of the regression line (which represents the change in the dependent variable for a unit change in the independent variable) must also be positive.

Therefore, option A is correct.

Cadmium, a heavy metal, is toxic to animals. Mushrooms, however, are able to absorb and accumulate cadmium at high concentrations. The Czech and Slovak governments have set a safety limit for cadmium in dry vegetables at 0.5 ppm. Below are cadmium levels for a random sample of the edible mushroom Boletus pinicoloa.0.24 0.92 0.59 0.19 0.62 0.330.16 0.25 0.77 0.59 1.33 0.32a) Perform a hypothesis test at the 5% significance level to determine if the meancadmium level in the population of Boletus pinicoloa mushrooms is greater than thegovernment’s recommended limit of 0.5 ppm. Suppose that the standard deviation ofthis population’s cadmium levels is o( = 0.37 ppm. Note that the sum of the data is 6.31 ppm. For this problem, be sure to: State your hypotheses, compute your test statistic, give the critical value.(b) Find the p-value for the test.

Answers

Answer:

hi

Step-by-step explanation:

In the word balloons the ratio of vowels consonants is

Answers

Answer:

  3 : 5

Step-by-step explanation:

vowels: a o o (3 of them)

consonants: b l l n s (5 of them)

The ratio of vowels to consonants is 3 : 5.

How would you describe the difference between the graphs of f(x) = x ^ 2 + 4 and g(y) = y ^ 2 + 4 OA. g(y) is a reflection of f(x) ) over the line y = 1 . O O B. g(y) is a reflection of f(x) ) over the line y=x 1 g(y) is a reflection of f(x) over the x-axis OD. g(y) is a reflection of f(x) over the .

Answers

x is replaced with Y, so it is a reflection across the line y = x

Answer:

y=x

Step-by-step explanation:

f(1)=-3
f(n)=-5*f(n-1)-7
f(2)=?
pls help lol. ​

Answers

Answer:

f(2)=8

Step-by-step explanation:

f(2)=(-5)*f(1)-7=

(-5)*(-3)-7=8

f(2)=8

An electrical engineer wishes to compare the mean lifetimes of two types of transistors in an application involving high-temperature performance. A sample of 60 transistors of type A were tested and were found to have a mean lifetime of 1827 hours and a standard deviation of 176 hours. A sample of 180 transistors of type B were tested and were found to have a mean lifetime of 1658 hours and a standard deviation of 246 hours. Let μX represent the population mean for transistors of type A and μY represent the population mean for transistors of type B. Find a 95% confidence interval for the difference μX−μY . Round the answers to three decimal places.

Answers

Answer:

add the decimals thats all

Step-by-step explanation:

Need help
6n - 3(2n - 5)

SHOW ALL WORK!

Answers

6n - 3(2n-5)

mutiply the bracket by -3

(-3)(2n)= -6n

(-3)(-5)= 15

6n-6n+15

0+15

answer:

15

6n-3(2n-5)
6n-(6n-15)
6n-6n+15
(6n-6n)+15
=15

A deck of cards contains 52 cards. They are divided into four suits: spades, diamonds, clubs and hearts. Each suit has 13 cards: ace through 10, and three picture cards: Jack, Queen, and King. Two suits are red in color: hearts and diamonds. Two suits are black in color: clubs and spades.

Use this information to compute the probabilities asked for below and leave them in fraction form. All events are in the context that three cards are dealt from a well-shuffled deck without replacement.

a. The first and second cards are both hearts.
b. The third card is an eight.
c. None of the three cards is an ace.

Answers

Answer:

a)  13/52    and the second  12/51

b) Two solutions:

b.1 if we did not picked up an eight in the first two cards   4/50

b.2 there is an eight i the two previous    3/59

c ) (48/52)*(47/51)*(46/50)

Step-by-step explanation:

Condition: Cards are taken out without replacement

a) Probability of first card is heart

There are 52 cards and 4 suits with the same probability , so you can compute this probability in two ways

we have  13 heart cards and 52 cards  then probability of one heart card is  13/52   = 0.25

or you have 4 suits, to pick up one specific suit the probability is 1/4 = 0,25

Now we have a deck of 51 card with 12 hearts, the probability of take one heart is : 12/51

b) There are 4 eight (one for each suit )   P =  4/50 if neither the first nor the second card was an eight of heart, if in a) previous we had an eight, then this probability change to 3/50

c) The probability of the first card different from an ace is 48/52 , the probability of the second one different of an ace is 47/51 and for the thirsd card is 46/50. The probability of none of the three cards is an ace is

(48/52)*(47/51)*(46/50)

A production process fills containers by weight. Weights of containers are approximately normally distributed. Historically, the standard deviation of weights is 5.5 ounces. (This standard deviation is therefore known.) A quality control expert selects n containers at random. How large a sample would be required in order for the 99% confidence interval for to have a length of 2 ounces?
a. n  15
b. n  16
c. n  201
d. n  226

Answers

Answer:

option (c) n = 201

Step-by-step explanation:

Data provided in the question:

Standard deviation, s = 5.5 ounce

Confidence level = 99%

Length of confidence interval = 2 ounces

Therefore,

margin of error, E = (Length of confidence interval ) ÷ 2

= 2 ÷ 2

= 1 ounce

Now,

E = [tex]\frac{zs}{\sqrt n}[/tex]

here,

z = 2.58 for 99% confidence interval

n = sample size

thus,

1 = [tex]\frac{2.58\times5.5}{\sqrt n}[/tex]

or

n = (2.58 × 5.5)²

or

n = 201.3561 ≈ 201

Hence,

option (c) n = 201

A news vendor sells newspapers and tries to maximize profits. The number of papers sold each day is a random variable. However, analysis of the past month's data shows the distribution of daily demand in Table 16. A paper costs the vendor 20C. The vendor sells the paper for 30C. Any unsold papers are returned to the publisher for a credit of IOC. Any unsatisfied demand is estimated to cost IOC in goodwill and lost profit. If the policy is to order a quantity equal to the preceding day's demand, determine the average daily profit of the news vendor by simulating this system. Assume that the demand for day 0 is equal to 32. Demand per day Probability30 .0531 .1532 .2233 .3834 .1435 .06

Answers

Let me think this through again and I will come back to you! 2.22 graph

A survey of 865 voters in one state reveals that 408 favor approval of an issue before the legislature.
Construct the 95 % confidence interval for the true proportion of all voters in the state who favor approval.

A) 0.435 < p < 0.508

B) 0.444 < p < 0.500

C) 0.471 < p < 0.472

D) 0.438 < p < 0.505

Answers

Answer: D) 0.438 < p < 0.505

Step-by-step explanation:

We know that the confidence interval for population proportion is given by :-

[tex]\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]

, where n= sample size

[tex]\hat{p}[/tex] = Sample proportion.

z* = critical value.

Given : A survey of 865 voters in one state reveals that 408 favor approval of an issue before the legislature.

i.e. n= 865

[tex]\hat{p}=\dfrac{408}{865}\approx0.4717[/tex]

Two-tailed critical avlue for 95% confidence interval : z* = 1.96

Then, the 95 % confidence interval for the true proportion of all voters in the state who favor approval will be :-

[tex]0.4717\pm (1.96)\sqrt{\dfrac{0.4717(1-0.4717)}{865}}\\\\\approx0.4717\pm 0.03327\\\\=(0.4717-0.03327,\ 0.4717+0.03327)=(0.43843,\ 0.50497)\approx(0.438,\ 0.505)[/tex]

Thus, the required 95% confidence interval : (0.438, 0.505)

Hence, the correct answer is D) 0.438 < p < 0.505

The Martian Colonies elect their government through a lottery. There are100,000 people living on Mars, and every year, a council of 99 co-equalleaders is randomly selected from the population. In how many ways canthe leadership be elected? Give your answer in terms of permutations orcombinations and explain your choice. You do not have to evaluate.

Answers

Answer:

The answer is a 100,000-choose-99 (a combination.)

[tex]P(100000, 99) = \displaystyle \left( \begin{array}{c}100000\cr 99\end{array}\right)[/tex].

Step-by-step explanation:

A combination [tex]C(n, r)[/tex] or equivalently [tex]\displaystyle \left(\begin{array}{c}n \cr r\end{array}\right)[/tex] gives the number of ways to choose [tex]r[/tex] out of [tex]n[/tex] elements.

A permutation [tex]P(n, r)[/tex] also gives the number of ways to choose [tex]r[/tex] out of [tex]n[/tex] elements. On top of that, it accounts for the order of the elements. Two elements in different order counts twice in a permutation, but only once in a combination.

The question emphasize that the council members are "co-equal." That implies that the order of the members don't really matter. Hence a combination with [tex]n = 100000[/tex] and [tex]r = 99[/tex] would be a more suitable choice.

The position vector for particle A is cos(t)i, and the position vector for particle B is sin(t)j. What is the difference in acceleration (i.e. the relative acceleration) between particle A and B at any time t? The acceleration vector of a particle moving in space is the second derivative of the position vector

Answers

Answer:

sin(t)j - cos(t)i

Step-by-step explanation:

Let's start with A:

Position vector = cos(t)i

Velocity vector = -sin(t)i (differentiating the position vector)

acceleration vector = -cos(t)i   (differentiating the velocity vector)

Then we go to B:

Position vector = sin(t)j

Velocity vector = cos(t)j

acceleration vector = -sin(t)j

Relative acceleration = -cos(t)i - (-sin(t)j) = sin(t)j - cos(t)i

About 20,000 steel cans are recycled every minute in the United States. Expressed in scientific notation, about how many cans are recycled in 48 hours?

Answers

Answer:

57,600,000

Step-by-step explanation:

Evaluate the integral Integral ∫ from (1,2,3 ) to (5, 7,-2 ) y dx + x dy + 4 dz by finding parametric equations for the line segment from ​(1​,2​,3​) to ​(5​,7​,- 2​) and evaluating the line integral of of F = yi + x j+ 3k along the segment. Since F is conservative, the integral is independent of the path.

Answers

[tex]\vec F(x,y,z)=y\,\vec\imath+x\,\vec\jmath+3\,\vec k[/tex]

is conservative if there is a scalar function [tex]f(x,y,z)[/tex] such that [tex]\nabla f=\vec F[/tex]. This would require

[tex]\dfrac{\partial f}{\partial x}=y[/tex]

[tex]\dfrac{\partial f}{\partial y}=x[/tex]

[tex]\dfrac{\partial f}{\partial z}=3[/tex]

(or perhaps the last partial derivative should be 4 to match up with the integral?)

From these equations we find

[tex]f(x,y,z)=xy+g(y,z)[/tex]

[tex]\dfrac{\partial f}{\partial y}=x=x+\dfrac{\partial g}{\partial y}\implies\dfrac{\partial g}{\partial y}=0\implies g(y,z)=h(z)[/tex]

[tex]f(x,y,z)=xy+h(z)[/tex]

[tex]\dfrac{\partial f}{\partial z}=3=\dfrac{\mathrm dh}{\mathrm dz}\implies h(z)=3z+C[/tex]

[tex]f(x,y,z)=xy+3z+C[/tex]

so [tex]\vec F[/tex] is indeed conservative, and the gradient theorem (a.k.a. fundamental theorem of calculus for line integrals) applies. The value of the line integral depends only the endpoints:

[tex]\displaystyle\int_{(1,2,3)}^{(5,7,-2)}y\,\mathrm dx+x\,\mathrm dy+3\,\mathrm dz=\int_{(1,2,3)}^{(5,7,-2)}\nabla f(x,y,z)\cdot\mathrm d\vec r[/tex]

[tex]=f(5,7,-2)-f(1,2,3)=\boxed{18}[/tex]

Suppose that in a bowling league, the scores among all bowlers are normally distributed with mean µ = 182 points and standard deviation σ = 14 points. A trophy is given to each player whose score is at or above the 97th percentile. What is the minimum score needed for a bowler to receive a trophy?

Answers

Answer:

209 points

Step-by-step explanation:

Mean points scored (μ) = 182 points  

Standard deviation (σ) = 14 points

The z-score for any given game score 'X' is defined as:  

[tex]z=\frac{X-\mu}{\sigma}[/tex]  

At, the 97th percentile of a normal distribution, the z-score, according to a z-score table, is 1.881.

Therefore, the minimum score, X, needed for a bowler to receive a trophy is:

[tex]1.881=\frac{X-182}{14}\\X=208.334[/tex]

Since only whole point scores are possible, X=209 points.

Final answer:

To find the minimum score at the 97th percentile for bowlers in a league, one must calculate the z-score for the 97th percentile and then apply the formula Score = μ + (z * σ) using the league's mean and standard deviation.

Explanation:

To find the minimum score needed for a bowler to receive a trophy (which is at or above the 97th percentile), we need to use the normal distribution properties. With a mean (μ) of 182 points and a standard deviation (σ) of 14 points, we can find the z-score corresponding to the 97th percentile using a z-table or a calculator with normal distribution functions. Once we have the z-score, we can use the formula:



Score = μ + (z * σ)



to calculate the score that corresponds to the 97th percentile.

Learn more about 97th percentile score here:

https://brainly.com/question/32902034

#SPJ3

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