The weights of the fish in a certain lake are normally distributed with a mean of 15 lb and a standard deviation of 5. If 4 fish are randomly selected, what is the probability that the mean weight will be between 12.6 and 18 lb.

The value for z  is 0.45

What are binomial words?

binomial. noun. bi no mi al b-n-m-l.: an equation consisting of a pair of terms joined by a plus or minus sign.: a biological species description consisting of 2 terms pursuant to the binomial nomenclature system.

To use the typical approximation we must first determine the binomial distribution's mean and standard deviation. The mean of a distribution that is bin is = np, while the standard deviations is = sqrt(np(1-p)). With n equals thirty & a p value 0.7, we get:

= np = 30(0.7) = 21 = [tex]\sqrt{(np(1-p)}[/tex] =[tex]\sqrt{(30(0.7)(1-0.7)}[/tex] = 2.24 = sqrt(30(0.7)(1-0.7)) = 2.24

Following that, we standardise X = 22 utilising the following equation:

z = (X - μ) / σ

With X = 22, X = 21, and X = 2.24, we obtain:

z = (22 - 21) / 2.24 = 0.45

Finally, we employ a conventional normal distribution tables (or calculator) to

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The expected number of calls in the first 30 minutes is 7.5

The Poisson distribution is frequently utilized to show the number of occasions that happen in a settled interim of time or space.

In this case, the number of calls to a Web benefit supplier during the hour between 6:00 and 7:00 p.m. is portrayed by a Poisson distribution with the mean rise to 15.

Since the Poisson distribution is memoryless, we will accept that the number of calls within the to begin with 30 minutes moreover takes after a Poisson conveyance with the mean rise to 15/2 = 7.5.

Typically since the expected number of occasions in a settled interim is relative to the length of the interim.

In this manner, the anticipated number of calls within the to begin with 30 minutes is 7.5. 

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Answer:

Step-by-step explanation:

I don't see the question.

The variable for an event that the number of heads in 50 tossed coins is a discrete variable. So, option(a) is right one.

A variable is a quantity whose value can be changed as a math problem. Thereare two types of variables:

Discrete variables represent counts, or the number of items in the collection. But continuous variables represent measurable quantities. Discrete variables are variables that have a measurable difference. For example, if X is equal to the number of miles (to the nearest mile) we drive to work, then X is a discrete random variable. We count the miles. Here we have an experiment of tossing a coin, We have to identify the variable used for the number of heads in 50 tossed coins. So, number of heads when flipping a coin is a discrete variable statement because once the coin is flipped, we will get head or tail result.

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The absolute minimum value of the function is -1 and the absolute maximum value is approximately 7.5417.

To find the absolute minimum and absolute maximum values of the function f(x) = x - 6x²  + 9x + 7 on the interval (-1, 4], we need to follow these steps:

1. Find the critical points by setting the derivative equal to zero.
2. Evaluate the function at the critical points and the endpoints of the interval.
3. Compare the values to find the absolute minimum and maximum.

Step 1: Find the critical points.
f'(x) = d/dx (x - 6x² + 9x + 7)
f'(x) = 1 - 12x + 9
To find the critical points, set f'(x) = 0:
0 = 1 - 12x + 9
12x = 10
x = 5/6

Step 2: Evaluate the function at the critical points and the endpoints of the interval.
f(-1) = -1 - 6(-1)²  + 9(-1) + 7 = -1
f(5/6) = (5/6) - 6(5/6)^2 + 9(5/6) + 7 ≈ 7.5417
f(4) = 4 - 6(4)²  + 9(4) + 7 = -87

Step 3: Compare the values.
Absolute minimum value: f(-1) = -1 (since -1 is the lowest value)
Absolute maximum value: f(5/6) ≈ 7.5417 (since 7.5417 is the highest value)

So, the absolute minimum value of the function is -1 and the absolute maximum value is approximately 7.5417.

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It is generally considered bad for the dependent variable y to be correlated with the error term e, even if the independent variable x is not.

This is because the presence of such correlation indicates that there may be omitted variables or measurement errors that are affecting both the dependent variable and the error term. In turn, this can lead to biased and inefficient estimates of the parameters in the regression model, as well as invalid hypothesis testing and confidence intervals.

To address this issue, it is recommended to carefully examine the data and model assumptions, consider alternative specifications or estimation methods, and possibly include additional variables or controls that may help explain the relationship between y and e.

This correlation between Y and E violates one of the key assumptions of the classical linear regression model, which states that the error term should be uncorrelated with both the dependent and independent variables. This violation can lead to biased and inconsistent estimators, ultimately affecting the reliability of the regression results.

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The new tuition for the fall will be $4,025 per semester. This is exactly what we get by using equation B, since: 1.15 • 3500 = 4025

The correct equation to find the new tuition for the fall is: B. 1.15 • 3500 = x

Here's why: The problem states that there is a 15% increase in tuition, which means that the new tuition will be the current tuition plus 15% of the current tuition. Mathematically, we can represent this as:

new tuition = current tuition + 15% of current tuition

Using x to represent the new tuition, and 3500 to represent the current tuition, we can write this equation as:

x = 3500 + 0.15(3500)

Simplifying the right side, we get:

x = 3500 + 525

x = 4025

Therefore, the new tuition for the fall will be $4,025 per semester. This is exactly what we get by using equation B, since: 1.15 • 3500 = 4025

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The test statistic t0 is -0.243. This can be answered by the concept of Standard deviation.

To find the test statistic t0, you can use the following formula:

t0 = (x - µ) / (s / √n)

where  x is the sample mean, µ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.

Plugging in the given values:

t0 = (7.9 - 8.0) / (1.3 / √10)

t0 = (-0.1) / (1.3 / 3.162)

t0 = -0.1 / 0.411

t0 = -0.243

After rounding to three decimal places, the test statistic t0 is -0.243.

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The 99% upper confidence bound for σ2 is $16,751.57.

To find the 99% upper confidence bound for σ2, we can use the chi-square distribution with n-1 degrees of freedom, where n is the sample size (in this case, n=45). The upper confidence bound can be found using the formula:

Upper Confidence Bound = (n-1) × sample variance / chi-square value

We need to find the chi-square value that corresponds to a 99% confidence level and n-1 degrees of freedom. From the chi-square distribution table, we can see that the value is 67.505.

Substituting the values, we get:

Upper Confidence Bound = (45-1) × 25,150 / 67.505
= 16,751.57

Therefore, the 99% upper confidence bound for σ2 is $16,751.57.

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The perimeter of the polygon is 61 feet.

A polygon is a two-dimensional geometric shape that is defined as a closed plane figure with three or more straight sides and angles. It is a flat shape made up of line segments that are connected end to end to form a closed shape.

The perimeter of a polygon is the total length of its sides. To find the perimeter of a polygon, we need to add up the lengths of all its sides.

In this problem, we are given the lengths of the sides of a polygon in feet: 12ft, 16ft, 9ft, 9ft, and 15ft.

To find the perimeter, we simply add up these lengths:

Perimeter = 12ft + 16ft + 9ft + 9ft + 15ft

Perimeter = 61ft

Therefore, the perimeter of the polygon is 61 feet. Note that the unit for the answer is feet, since all the lengths were given in feet.

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we need to know the value of S₇(5) to determine the value of I.

I = S₇(0) + S₇(7) - 2S₇(5) = 9 + 7 - 2S₇(5) = 16 - 2S₇(5)

We can use the properties of integrals to determine the value of I:

I = ∫_0⁵ f(x)dx + ∫_5⁷ f(x)dx

Using the given information, we can express the two integrals on the right-hand side in terms of S₇(0) and S₇(5):

∫_0⁵ f(x)dx = S₇(0) - S₇(5)

∫_5⁷ f(x)dx = S₇(7) - S₇(5)

Substituting these expressions into the equation for I, we get:

I = (S₇(0) - S7(5)) + (S₇(7) - S₇(5))

Simplifying this expression, we get:

I = S₇(0) + S₇(7) - 2S₇(5)

Now we can use the given values of S₇(0), S₇(5), and S₇(7) to find I:

I = S₇(0) + S₇(7) - 2S₇(5) = 9 + 7 - 2S₇(5) = 16 - 2S₇(5)

Therefore, we need to know the value of S₇(5) to determine the value of I.

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Answer:

Below

Step-by-step explanation:

formula for area of circle: A = (pie)(r)^2

1. 5 cm radius:

A = (pie)(r)^2

A = (pie)(5)^2

A = 78.54 and 78.5 cm^2

2. 6 cm radius:

A = (pie)(r)^2

A = (pie)(6)^2

A = 113.04 cm^2

3. 9 cm radius:

A = (pie)(r)^2

A = (pie)(9)^2

A = 254.34 cm^2

10. 10 cm radius:

A = (pie)(r)^2

A = (pie)(10)^2

A = 314 cm^2

Hope this helps^^

The sum of the given infinite series 11 +2 + 4/11 + 8/121 + ...  is 121.

A geometric series is a sequence of numbers in which each term after the first is obtained by multiplying the preceding term by a fixed nonzero constant called the common ratio.

The given series is a geometric series with the first term being 11 and the common ratio being 2/11. Thus, the sum of the infinite series is given by

S = a / (1 - r)

where a is the first term and r is the common ratio.

Substituting the values, we get

S = 11 / (1 - 2/11) = 11 / (9/11) = 121

Hence, the sum of the given infinite series is 121.

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The given question is incomplete, the complete  question is:

Find the sum of the following infinite series. If it is divergent, type "Diverges" or "D". 11 +2 + 4/11 + 8/121 + ...

The standard deviation of the sampling distribution of the sample proportion can be calculated using the formula: σp = sqrt[p(1-p)/n]

where p is the expected proportion of red blossoms in the hybrid plants, n is the sample size, and sqrt represents the square root.

Here, p = 0.15, n = 50, and the sample proportion of red blossoms is 0.22.

So, the standard deviation of the sampling distribution of the sample proportion is:

σp = sqrt[(0.15)(1-0.15)/50]

= sqrt[(0.1275)/50]

= 0.051

Therefore, the standard deviation of the sampling distribution of the sample proportion is approximately 0.051.

Answer options B, 0.051, is the correct answer.

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When a marketing manager surveys a few of the customers for the purpose of drawing a conclusion about the entire list of customers, she is applying inferential statistics.

Hence option a is the correct answer.

Inferential statistics is referred to that field of statistics which uses analytical tools to draw conclusions about a population by examining (or, surveying) random samples (taken from the population).

Inferential statistics generalizes the observations derived from the sample as the observations from the population.

Here the marketing manager surveys a few of the customers who work as representation of the population of customers to draw conclusions, that is the observation is generalized for the entire list of customers though it is based on replies from a few customers.

Thus, the marketing manager is applying inferential statistics.

Hence option a is the correct answer.

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a) The t critical values are -1.708 and  1.708

b) The t critical values are -1.782 and  1.782

What is t-statistic ?

The t-statistic in statistics measures how far an estimated value of a parameter deviates from its hypothesised value in relation to its standard error.

T symbol in statistics mean Test statistic for t-test ( t-score )

a) At α = 0.10,  df=14+13-2 = 25( two tailed)

t critical values are -1.708 and  1.708

b) At α = 0.10,  

df= smaller(n1-1, n2-1)= smaller(14-1, 13-1)= smaller(13, 12) = 12

t critical values are -1.782 and  1.782

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The conditional probability that you picked the fake coin given that you got heads twice is 4/(3n-1).

Let E be the case where you choose the bogus coin and F be the case where you got heads twice. We wish to calculate P(E|F), which is the likelihood that you chose the fake coin given that you received heads twice.

By Bayes' theorem, we have:

P(E|F) = P(F|E)P(E) / P(F)

We can calculate each term on the right-hand side as follows:

P(F|E) = 1, Because the fake coin contains heads on both sides and always results in two heads when flipped.

P(E) = 1/n, since there is only one fake coin among n coins.

P(F) = P(F|E)P(E) + P(F|not E)P(not E), where not E is the event that you picked a normal coin. We can calculate:

P(F|not E) = (n-1) * (1/2)^2 = (n-1)/4, Because each normal coin has a 50% chance of revealing heads on each given flip and there are n-1 normal coins

P(not E) = (n-1)/n, since there are n-1 normal coins among n coins.

Therefore, we have:

P(F) = 1 * (1/n) + (n-1)/4 * (n-1)/n = (3n-1)/(4n)

Substituting these values into Bayes' theorem, we get:

P(E|F) = 1 * (1/n) / ((3n-1)/(4n)) = 4/(3n-1)

Thus, the conditional probability that you picked the fake coin given that you got heads twice is 4/(3n-1).

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Answer:

63

Step-by-step explanation:

We can find the other multiples of a number by adding or subtracting the number.

n is less than 70 and is divisible by 7, which means we need to subtract 7 from 70.

70 - 7 = 63

The series is convergent according to Ratio test.

To determine whether the series Σ n=1 (-1)ⁿ + 1 n⁶ 6ⁿ/n! is convergent or divergent, we can use the Ratio Test. First, we need to find the limit of the ratio of consecutive terms as n approaches infinity.

|an+1|/|an| = (n+1)⁶ 6^(n+1)/(n+1)! * n!/n⁶ 6ⁿ

= (n+1)⁶/6n⁶ * 6/((n+1)(n)(n-1)(n-2)(n-3)(n-4))

= [(n+1)/n]⁶ * 6/[(n+1)(n)(n-1)(n-2)(n-3)(n-4)]

As n approaches infinity, the first term in the product approaches 1, and the second term approaches 0. Therefore, the limit of the ratio of consecutive terms is 0.

Since the limit of the ratio of consecutive terms is less than 1, the series is convergent by the Ratio Test.

The value of the limit lim n--> [infinity] |an + 1|/|an| is 0, as we found in the previous calculation. This limit represents the rate at which the terms of the series Σ n=1 (-1)ⁿ + 1 n⁶ 6ⁿ/n! approach zero as n approaches infinity.

Since the limit is 0, the terms of the series approach zero very quickly as n becomes large, which supports the conclusion that the series is convergent.

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By examining the diagonal of the matrix, we can compare the correlations between different constructs measured using the same method to the correlations between the same construct measured using different methods.

The MTMM matrix, or the Multi-Trait Multi-Method matrix, is a popular tool used in psychology and social sciences to assess the validity of measurements.

To understand how discriminate validity is estimated using the MTMM matrix, let's first explore what the matrix is. The MTMM matrix is a table that displays the correlations between multiple traits (constructs) and multiple methods of measuring these traits.

Now, to estimate discriminate validity, we need to examine the diagonal of the matrix. The diagonal represents the correlations between each construct and the same method of measurement. For example, the correlation between intelligence measured using self-report and intelligence measured using objective tests.

Discriminate validity can be assessed by comparing these correlations to the correlations between different constructs measured using the same method.

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Based on the information provided, it appears that the government directed innovation activities during the Vietnam War had a unique program that gave qualifying applicants the opportunity to work at the US Government Office of Research instead of being drafted for combat. This program had a specific goal, which may have been to support innovation efforts during the war or to provide an alternative service opportunity for those who did not want to fight in combat.



Overall, this program is an interesting example of how the government can direct innovation activities through specific programs and initiatives. It also demonstrates how random selection can be used to determine who participates in these programs, which may have implications for how successful they are in achieving their goals.
In this scenario, the government implemented a program during the Vietnam War that allowed qualifying applicants to work at the US Government Office of Research as an alternative to being drafted for combat. The program's objective was to promote innovation and increase patenting by utilizing the skills and expertise of these individuals. The government randomly selected the candidates who would be offered the opportunity to work in the Office of Research, ensuring a fair selection process. This program highlights the potential impact of government-directed innovation activities on patenting and showcases how the government can actively support and encourage advancements in technology and research.

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Option (1) is correct. The minimum weight an interpreter can guess without  winning a prize is 138 pounds and the maximum weight is 146 pounds.  

 Linear equations are first-order equations. Linear equations are defined for the lines of the coordinate system. If an equation has a homogeneous variable of degree 1 (that is only one variable),  it is called a linear equation in one variable. A linear equation can have more than one variable.  

The correct equation would be:  a) |x - 142| ≤ 4

Explanation:

The carnival performer claims to be able to guess a person's weight within 4 kilograms of their actual weight, which means that the difference between the guessed weight and the actual weight must not be  more than 4 kilograms.

Let x be the weight of the carnival performer. In this case the difference between x and 142 cannot be  more than 4 pounds. It can be written as:

|x - 142| ≤ 4

This inequality means that x can be any weight within 4 pounds of 142, giving the range:

142 - 4 ≤ x ≤ 142 4

138 ≤ x ≤ 146

Therefore, the minimum weight an interpreter can guess without  winning a prize is 138 pounds and the maximum weight is 146 pounds.

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The calculated exact value of x  in the right triangle is 5√5

From the question, we have the following parameters that can be used in our computation:

Similar triangles

Using the theorem of corresponding sides in similar triangles, we have the following proportion

x/15 = 5/x

When both sides of the equation are cross multplied, we have

x^2 = 75

Take the square root of both sides

So, we have

x = 5√5

Hence, the exact value of x is 5√5

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Answer: greater than

Step-by-step explanation:

p(spinning even) = [tex]\frac{2}{5}[/tex] = 0.4

p(drawing even card) = [tex]\frac{5}{13}[/tex] = 0.384615384615

so 2/5 is greater than 5/13

Answer:

True

Step-by-step explanation:

27 = 3 x 9

0.9 = 9 x 0.1

27 ÷ 0.9

= 27/0.9

= (3 x 9)/(9 x 0.1)

= 3/0.1

= 3/0.1 x 10/10

= (3 x 10)/(0.1 x 10)

= 30/1

= 30

The 80% confidence interval for the meantime is 5.660 to 6.340 hours.

To calculate the 80% confidence interval for the meantime, we will use the following formula:

CI = Mean ± (Z-score * (Standard deviation / √Sample size))

Here, Mean = 6 hours, Standard deviation = 1.3 hours, and Sample size = 24.

For an 80% confidence interval, the Z-score is 1.282 (from the standard normal distribution table).

Now, plug in the values:

CI = 6 ± (1.282 * (1.3 / √24))

CI = 6 ± (1.282 * (1.3 / 4.899))

CI = 6 ± (1.282 * 0.265)

CI = 6 ± 0.340

The 80% confidence interval for the meantime is 5.660 to 6.340 hours.

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Answer:

4.8 squared meters

Step-by-step explanation:

divide the area value by 10,000

The statement is true. If f and g are decreasing on an interval I, then their sum, f + g, is also decreasing on the interval I.

Statement: If f and g are decreasing on an interval I, then f + g is decreasing on I.
Answer: True.

Explanation:
1. Since f is decreasing on interval I, this means that for any x1, x2 in I, if x1 < x2, then f(x1) > f(x2).
2. Similarly, since g is decreasing on interval I, for any x1, x2 in I, if x1 < x2, then g(x1) > g(x2).
3. Now, let's consider the function h(x) = f(x) + g(x).
4. We need to show that h is decreasing on interval I. For any x1, x2 in I with x1 < x2, we want to show that h(x1) > h(x2).
5. From steps 1 and 2, we have f(x1) > f(x2) and g(x1) > g(x2).
6. Adding these inequalities, we get f(x1) + g(x1) > f(x2) + g(x2), which means h(x1) > h(x2).
7. So, h(x) = f(x) + g(x) is decreasing on interval I.

The statement is true. If f and g are decreasing on an interval I, then their sum, f + g, is also decreasing on the interval I.

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The translation used to create the image on the graph is (5, -4), which means that all points on the original figure have been moved 5 units to the right and 4 units down.

A graph is a visual representation of data or information, often displayed on a coordinate system with points or lines indicating the values or relationships between variables. It can be used to show trends, patterns, and comparisons.

Translation is a type of transformation in geometry that involves moving an object or shape from one position to another without changing its size, shape, or orientation. It is also known as a slide.

According to the given information:

Based on the graph, we can see that points A have been translated 5 units to the right and 4 units down to create point A'. This means that a translation of (5, -4) was used to create the image.

Similarly, point B has been translated 5 units to the right and 6 units up to create point B', so a translation of (5, 6) was used. Point C has been translated 5 units to the right and 3 units up to create point C', so a translation of (5, 3) was used. Finally, point D has been translated 5 units to the right and 4 units down to create point D', so a translation of (5, -4) was used again.

Therefore, the translation used to create the image is (5, -4).

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To find the expected value and variance of a negative binomial random variable with moment generating function mx(t) = (1 - p)^r / (1 - pe^t)^r, we need to use the following formulas:

The nth moment of a random variable is given by mx^(n)(0), the nth derivative of the moment generating function evaluated at t = 0.

The expected value of a random variable is given by mx^(1)(0).

The variance of a random variable is given by mx^(2)(0) - [mx^(1)(0)]^2.

Using these formulas, we can find the expected value and variance of the negative binomial random variable.

First, let's find the first two derivatives of the moment generating function:

mx'(t) = r(1-p)^rpe^t / (1-pe^t)^(r+1)

mx''(t) = r(1-p)^rpe^t(r+1-pe^t) / (1-pe^t)^(r+2)

Now we can evaluate the moment generating function and its derivatives at t = 0 to find the expected value and variance:

mx(0) = (1 - p)^r / (1 - p)^r = 1

mx'(0) = r(1-p)^r p / (1-p)^(r+1)

mx''(0) = r(r+1)(1-p)^r p / (1-p)^(r+2) + r(1-p)^r p / (1-p)^(r+1)

Using the formulas for the expected value and variance, we have:

E[X] = mx'(0) = r(1-p) / p

Var[X] = mx''(0) - [mx'(0)]^2 = r(1-p) / p^2

Therefore, the expected value of the negative binomial random variable is E[X] = r(1-p) / p, and the variance is Var[X] = r(1-p) / p^2, where p and r are the parameters of the distribution.

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