Suppose it is known that 10% of all people in Texas have a specific blood type. Suppose we take a random sample of 500 Texas residents. We want to find chance that fewer than 40 Texas residents in this sample have that blood type. In the next 4 questions, find the box model, the average and standard deviation of the box and use these values to find the expected value and standard error. Then calculate the associated chance of having fewer than 40 Texas residents in the sample with that specific blood type. Suppose you calculated EV and SE correctly in the previous two problems. The chance that fewer than 40 Texas residents in this sample have that blood type is the area under the normal curve to the:

Answer: C represents a function

Step-by-step explanation: It represents a function because there is exactly one range for each domain, and only one. In mathematics, an algebraic function is a function that can be defined as the root of a polynomial equation. Quite often algebraic functions are algebraic expressions using a finite number of terms, involving only the algebraic operations addition, subtraction, multiplication, division, and raising to a fractional power.

Answer:2

4 th root of 1024 is 5

Since 4 x4x4x4x4=1024

So 1+2x=5

-1 PN both sides

2x= 4

Divide by 2

X=2

Step-by-step explanation:

There are 54 two-digit numbers greater than 45. This is calculated by finding the range of valid two-digit numbers (46 to 99) or carefully counting possible combinations without including 45.

The two-digit numbers greater than 45 are any numbers from 46 to 99. We can find the amount of these numbers by subtracting 45 from 99. So, there are 54 two-digit numbers greater than 45.

Another way to visualize this is by considering the two-digit possibilities. The first digit can range from 4 to 9 (six possibilities), and the second digit can range from 0 to 9 (ten possibilities). However, since 40-45 are not included, we subtract 5 from the total possibilities, resulting in 60 (=6*10) -5 = 55. Therefore, it seems that we have one number too many, but we must not forget that 45 itself is not included, hence the total numbers exceeding 45 are 54 (55-1).

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Answer:

Experiement lacked blindness concept

Step-by-step explanation:

In good experiments, the results are totally unbiased and unknown to anyone, even to those conducting the experiment.

In the given case, the interviewer had an idea about which group had gone for meditation so it was obvious that they would yield less anxiety.

Here the concept of blinding was missing, which is essential for a good and fair experiment. A good experiemnt is a double blinded experiement or atleast it should be single blinded

Answer:

d

Step-by-step explanation:

C is the center of a circle. Find the length of arc AB to two decimal points

Answer:

d

Step-by-step explanation:

s=13.68

Answer:

13%

Step-by-step explanation:

There are 100 squares and 13 are shaded so

13/100=

13%

Answer:

13%

Step-by-step explanation:

Answer:

use 6cm twice and that adds up to 12cm .six is the minimal possible number

A ruler designed to measure lengths from one unit to twelve units with the minimum number of marks would only have marks at every unit. This results in only eleven markings (from 1 to 11), as the 0 marks the start and the twelfth unit marks the end.

The subject of the student's question pertains to the design of a ruler with the minimum possible number of marks that can measure lengths from one to twelve units. To achieve this, the ruler should only be marked at every unit. This way, there would be only eleven marks (1-11), as the 0 marks the start of the ruler and the twelfth unit is considered the end of the ruler but does not require a mark. Therefore, only the spaces between these numbers need to be marked to enable measurement all the way up to twelve units.

In practice, such a ruler is less precise than a ruler with more marks as the latter can measure smaller lengths more accurately. However, the task demands the bare minimum for a measure from 1 to 12, thus we have eleven marks.

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Answer:

(0.339, 0.391)

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 1295, \pi = \frac{473}{1295} = 0.365[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.365 - 1.96\sqrt{\frac{0.365*0.635}{1295}} = 0.339[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.365 + 1.96\sqrt{\frac{0.365*0.635}{1295}} = 0.391[/tex]

So the correct answer is:

(0.339, 0.391)

Answer:

The 95% confidence (and interpret) the proportion of all American adults of European an- cestry who dislike the taste of cilantro

(  0.2552  , 0.2709)

b) The lower bound for the proportion of all American adults of European ancestry who dislike the taste of cilantro is  0.2552

Step-by-step explanation:

Explanation:-

Given data a survey of 12087 American adults of European ancestry asked whether they like or dislike the taste of cilantro.

large sample size 'n' = 12087 American adults

in survey A total of 3181 said that they dislike the taste of cilantro.

so The sample proportion 'p' = [tex]\frac{3181}{12087} = 0.2631[/tex]

a) Estimate with 95% confidence (and interpret) the proportion of all American adults of European ancestry who dislike the taste of cilantro.

[tex](p - 1.96 \sqrt{\frac{pq}{n} } ,p + 1.96\sqrt{\frac{pq}{n} } )[/tex]

[tex](0.2631 - 1.96 \sqrt{\frac{0.2631 X 0.7369}{12087} } ,0.2631 + 1.96\sqrt{\frac{0.2631 X 0.7369 }{12087} } )[/tex]

(0.2631 - 0.00784 , 0.2631 + 0.00784 )

(  0.2552  , 0.2709)

b) The lower bound for the proportion of all American adults of European ancestry who dislike the taste of cilantro is  0.2552

We are 95% confident that the proportion of all American adults of European ancestry who dislike the taste of cilantro is between 25.5% and 27.1%, and at least 25.5% dislike the taste.

This question is related to confidence intervals in statistics. To compute a confidence interval for a population proportion, we mainly need the sample proportion and the size of the sample. Here, the proportion is the number of respondents that dislike cilantro (3181) divided by the total number of respondents (12087).

Thus, the sample proportion (value of p) is 3181/12087 = 0.263 or 26.3%.

The formula for a confidence interval is:

CI = p +/- Z * sqrt[ (p(1-p)) / n ],

where Z is the Z-score (for 95% confidence, Z = 1.96), p is the sample proportion, and n is the sample size.

Applying the values, we get:

CI = 0.263 +/- 1.96 * sqrt[ (0.263)(1 - 0.263) / 12087 ]

After calculation, the 95% confidence interval is about (0.255, 0.271). This means we are 95% confident that the proportion of all American adults of European ancestry who dislike the taste of cilantro is between 25.5% and 27.1%.

For the lower bound, we can take the lower limit of our confidence interval, which is 0.255 or 25.5%. This means we are 95% confident that at least 25.5% of all American adults of European ancestry dislike the taste of cilantro.

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Step-by-step explanation:

W(x) = (10x⁴ − 8) (30x + 25)^0.5

A) Take log of both sides.

ln(W) = ln[(10x⁴ − 8) (30x + 25)^0.5]

ln(W) = ln(10x⁴ − 8) + ln[(30x + 25)^0.5]

ln(W) = ln(10x⁴ − 8) + 0.5 ln(30x + 25)

Take derivative.

W' / W = 40x³ / (10x⁴ − 8) + 0.5 (30) / (30x + 25)

W' / W = 20x³ / (5x⁴ − 4) + 3 / (6x + 5)

W' = W [20x³ / (5x⁴ − 4) + 3 / (6x + 5)]

W'(x) = (10x⁴ − 8) (30x + 25)^0.5 [20x³ / (5x⁴ − 4) + 3 / (6x + 5)]

B) Evaluate at x = 0.

W'(0) = (0 − 8) (0 + 25)^0.5 [0 / (0 − 4) + 3 / (0 + 5)]

W'(0) = (-8) (5) (0 + 3/5)

W'(0) = -24

Answer:

[tex]\textsf{A)}\quad W'(x) = (10x^4 - 8) \cdot (30x + 25)^{0.5} \left(\dfrac{20x^3}{5x^4 - 4} + \dfrac{3}{6x + 5} \right)[/tex]

[tex]\textsf{B)}\quad W'(0)=-24[/tex]

Step-by-step explanation:

Given function:

[tex]W(x) = (10x^4 - 8) \cdot (30x + 25)^{0.5}[/tex]

Take the natural logarithm of both sides:

[tex]\ln \left(W(x)\right) = \ln \left( (10x^4 - 8) \cdot (30x + 25)^{0.5} \right)[/tex]

Use properties of logarithms to simplify:

[tex]\ln \left(W(x)\right) = \ln (10x^4 - 8) +\ln(30x + 25)^{0.5} \\\\\\ \ln \left(W(x)\right) = \ln (10x^4 - 8) +0.5 \ln(30x + 25)[/tex]

Differentiate both sides with respect to x:

[tex]\dfrac{d}{dx} \ln \left(W(x)\right) = \dfrac{d}{dx} \left( \ln (10x^4 - 8) + 0.5 \ln (30x + 25) \right)[/tex]

Apply the chain rule on the right-hand side:

[tex]\dfrac{W'(x)}{W(x)} = \dfrac{1}{10x^4 - 8} \cdot \dfrac{d}{dx} (10x^4 - 8) + 0.5 \cdot \dfrac{1}{30x + 25} \cdot \dfrac{d}{dx} (30x + 25) \\\\\\ \dfrac{W'(x)}{W(x)} = \dfrac{1}{10x^4 - 8} \cdot (40x^3) + 0.5 \cdot \dfrac{1}{30x + 25} \cdot (30) \\\\\\ \dfrac{W'(x)}{W(x)} = \dfrac{40x^3}{10x^4 - 8} + \dfrac{15}{30x + 25} \\\\\\ \dfrac{W'(x)}{W(x)} = \dfrac{2(20x^3)}{2(5x^4 - 4)} + \dfrac{5(3)}{5(6x + 5)} \\\\\\ \dfrac{W'(x)}{W(x)} = \dfrac{20x^3}{5x^4 - 4} + \dfrac{3}{6x + 5}[/tex]

Multiply both sides by W(x) to solve for W'(x):

[tex]W'(x) = W(x) \left(\dfrac{20x^3}{5x^4 - 4} + \dfrac{3}{6x + 5} \right)[/tex]

Substitute W(x) back in:

[tex]W'(x) = (10x^4 - 8) \cdot (30x + 25)^{0.5} \left(\dfrac{20x^3}{5x^4 - 4} + \dfrac{3}{6x + 5} \right)[/tex]

Therefore, the derivative W'(x) is:

[tex]W'(x) = (10x^4 - 8) \cdot (30x + 25)^{0.5} \left(\dfrac{20x^3}{5x^4 - 4} + \dfrac{3}{6x + 5} \right)[/tex]

[tex]\dotfill[/tex]

To find W'(0), substitute x = 0 into W'(x):

[tex]W'(0) = (10(0)^4 - 8) \cdot (30(0) + 25)^{0.5} \left(\dfrac{20(0)^3}{5(0)^4 - 4} + \dfrac{3}{6(0) + 5} \right) \\\\\\ W'(0) = (0 - 8) \cdot (0 + 25)^{0.5} \left(\dfrac{0}{0 - 4} + \dfrac{3}{0 + 5} \right) \\\\\\ W'(0) = (- 8) \cdot (25)^{0.5} \cdot \left( \dfrac{3}{5} \right) \\\\\\ W'(0) = (- 8) \cdot 5 \cdot \dfrac{3}{5} \\\\\\ W'(0)=-24[/tex]

Therefore, the value of W'(0) is -24.

Answer:

a, -b

Step-by-step explanation:

When x is a, the function becomes

[tex]f(a)=3(a-a)(a+b)[/tex]

as you see, a-a is 0, and as your whole function is multiplied by this, it makes it 0.

[tex]f(-b)=3(-b-a)(-b+b)[/tex]

As you see -b+b is 0, and once again, this would make the whole function 0.

Answer:

i believe it is 4 but i'm not so sure

Step-by-step explanation:

:)

The graph of g(x)=(x-2)^2+3 compared to the graph of f(x)=x^2 is translated 2 units to the right and 3 units upwards.

To understand the transformation of graphs in mathematical terms, consider the initial function f(x) = x^2. The transition to the new function g(x)=(x-2)^2+3 is a result of a shift or translation of the graph. This transformation behaves as per the following rule: g(x) = f(x-h)+k where 'h' units is the horizontal displacement and 'k' units is the vertical displacement.

In the function g(x), x shifts two units to the right (as indicated by (x-2)) and three units upward (as indicated by +3).

So, the correct answer is 2 units right and 3 units up.

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Answer:

A. Brand A has a higher average price than brand B.

D. Brand A's prices are less spread out than brand B's prices.

Step-by-step explanation:

We are given the means and standard deviations for samples of prices from two  different brands of shoes below;

 Brand A                                                                  Brand B

Mean : $50                                                           Mean : $40

Standard deviation : $5                                  Standard deviation : $8    

Now, from the given statements;

Statement A is correct that Brand A has a higher average price than brand B because as given above Mean of Brand A ($50) > Mean of Brand B ($40).

Also, Statement D is correct that Brand A's prices are less spread out than brand B's prices because the Variance of Brand A is less than the variance of Brand B, i.e.;

    Variance of Brand A = [tex]5^{2}[/tex] = $25

    Variance of Brand B = [tex]8^{2}[/tex] = $64

Clearly, $25 < $64, so statement D is also correct.

Therefore, the two true statements are Statement A and Statement D.

Final answer:

A. Brand A has a higher average price than brand B.

D. Brand A's prices are less spread out than brand B's prices.

Explanation:

The true statements are that Brand A has a higher average price and less variability in prices than Brand B, which is represented by a lower standard deviation for Brand A.

To expand on these points:

Brand A has a mean price of $50 which is higher than Brand B's mean price of $40, confirming that Brand A has a higher average price (Statement A).

Brand A's standard deviation is $5, while Brand B's standard deviation is $8. A standard deviation is a measure of spread or variability in a set of data. The fact that Brand A's standard deviation is lower indicates that its prices are less variable and more closely clustered around the mean, hence less spread out compared to Brand B (Statement D).

Answer:

k= 13*3-2

k= 39-2

k=37 is the required answer

Answer:

k = 37

Step-by-step explanation:

[tex]k = 13t - 2 \\ \therefore \: k = 13 \times 3 - 2 \\ \therefore \: k = 39 - 2 \\ \huge \red{ \boxed{ \therefore \: k = 37}}[/tex]

Answer:

The answer is (A)

Answer:

The answer is A.

Step-by-step explanation:

This is because the plus sign after the first mixed number gets multiplied to the second mixed number. When a plus sign gets multiplied to something that is negative already, then the answer is negative, so the equation will still stay the same and be -3 1/8 - 2 1/2.

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Answer:

The expected repair cost is $3.73.

Step-by-step explanation:

The random variable X is defined as the number of defectives among the 4 items sold.

The probability of a large lot of items containing defectives is, p = 0.09.

An item is defective irrespective of the others.

The random variable X follows a Binomial distribution with parameters n = 9 and p = 0.09.

The repair cost of the item is given by:

[tex]C=3X^{2}+X+2[/tex]

Compute the expected cost of repair as follows:

[tex]E(C)=E(3X^{2}+X+2)[/tex]

        [tex]=3E(X^{2})+E(X)+2[/tex]

Compute the expected value of X as follows:

[tex]E(X)=np[/tex]

         [tex]=4\times 0.09\\=0.36[/tex]

The expected value of X is 0.36.

Compute the variance of X as follows:

[tex]V(X)=np(1-p)[/tex]

         [tex]=4\times 0.09\times 0.91\\=0.3276\\[/tex]

The variance of X is 0.3276.

The variance can also be computed using the formula:

[tex]V(X)=E(Y^{2})-(E(Y))^{2}[/tex]

Then the formula of [tex]E(Y^{2})[/tex] is:

[tex]E(Y^{2})=V(X)+(E(Y))^{2}[/tex]

Compute the value of [tex]E(Y^{2})[/tex] as follows:

[tex]E(Y^{2})=V(X)+(E(Y))^{2}[/tex]

          [tex]=0.3276+(0.36)^{2}\\=0.4572[/tex]

The expected repair cost is:

[tex]E(C)=3E(X^{2})+E(X)+2[/tex]

         [tex]=(3\times 0.4572)+0.36+2\\=3.7316\\\approx 3.73[/tex]

Thus, the expected repair cost is $3.73.

Median: 133.5

Lower/First quartile: 128

Upper/Third quartile: 139

Interquartile range: 139 - 128 = 11

so your interquartile range is 11

Answer:

(a)Mean=9

(b)Median=9.5

(c)Mode=12

(d)Standard Deviation=2.53

Step-by-step explanation:

The sample of the number of vehicles that proceeded through the intersection after the light changed for 6 days during a 1 month period is given below:

6 12 7 12 8 9

(a)Mean

[tex]Mean=\frac{6+12+ 7+ 12+ 8+ 9}{6} \\=\frac{54}{6} \\Mean=9[/tex]

(b)Median

First, arrange in ascending order

6,7,8,9,12,12

Since we have two terms in the middle, we take the average.

[tex]Median=\frac{8+9}{2}\\Median=8.5[/tex]

(c)Mode

The mode is the number with the highest frequency. The mode number of cars is 12.

(d)Standard Deviation

[tex]S.D.=\sqrt{\dfrac{\sum_{i=1}^{n}(x-\bar{x})^2}{n-1}}[/tex]

[tex]S.D.=\sqrt\frac{(6-9)^2+(7-9)^2+(8-9)^2+(9-9)^2+(12-9)^2+(12-9)^2}{6-1}[/tex]

[tex]=\sqrt{6.4} \\S.D.=2.53[/tex]

Answer:

[tex]1100 \text{feet}^3[/tex]

Step-by-step explanation:

GIVEN: A swimming pool is circular with a [tex]20\text{ feet}[/tex] diameter. The depth is constant along east-west lines and increases linearly from [tex]1\text{ feet}[/tex] at the south end to [tex]6\text{ feet}[/tex] at the north end.

TO FIND: Find the volume of water in the pool.

SOLUTION:

Consider the image attached.

when two similar figures are attached a new cylinder is formed. volume of swimming pool is half of volume of new cylinder formed.

radius of new cylinder [tex]=\frac{\text{diameter}}{2}=\frac{20}{2}=10\text{ feet}[/tex]

height of new cylinder [tex]=6+1=7\text{ feet}[/tex]

volume of cylinder [tex]=\pi r^2h=\frac{22}{7}\times(10)^27[/tex]

                               [tex]=2200\text{ feet}^3[/tex]

Volume of swimming pool [tex]=\frac{\text{volume of cylinder}}{2}=\frac{2200}{2}[/tex]

                                           [tex]=1100\text{ feet}^3[/tex]

Hence volume of water in the pool is [tex]1100 \text{feet}^3[/tex].

Final answer:

To find the volume of water in a swimming pool with varying depths, calculate the volume by considering different height sections of the pool.The volume of water in the pool is approximately 13,287 ft³.

Explanation:

A swimming pool is circular with a 20-ft diameter. The depth is constant along east-west lines and increases linearly from 1 ft at the south end to 6 ft at the north end.

Given the pool's dimensions, you can calculate the volume of water in the pool by breaking it into sections of different heights.

The volume of water in the pool is approximately 13,287 ft³.

Answer:

Galloping speed Y=179.984-0.076 weight X

Step-by-step explanation:

The required equation is

y=a+bx

where y is galloping speed and x is weight of animal.

We have to estimate intercept a and slope b.

x                  y         xy       x²

25    191.5 4787.5 625

35     184.7 6464.5 1225

50    175.8 8790 2500

75     162.2 12165 5625

500  124.9 62450 250000

1000 113.2 113200 1000000

sumx=1685

sumy=952.3

sumxy=207857

sumx²=1259975

[tex]slope=b=\frac{n(sumxy)-(sumx)(sumy)}{nsumx^{2}-(sumx)^{2} }[/tex]

[tex]slope=b=\frac{6(207857)-(1685)(952.3)}{6*(1259975)-(1685)^{2} }[/tex]

[tex]slope=b=\frac{-357483.5}{4720625}[/tex]

slope=b=-0.07573.

intercept=a=ybar-b*xbar

[tex]ybar=\frac{sumy}{n}[/tex]

[tex]ybar=\frac{952.3}{6}[/tex]

ybar=158.7167

[tex]xbar=\frac{sumx}{n}[/tex]

[tex]xbar=\frac{1685}{6}[/tex]

xbar=280.8333

intercept=a=ybar-b*xbar

intercept=a=158.7167-(-0.07573)*280.8333

intercept=a=158.7167+21.2675

intercept=a=179.9842

rounding intercept and slope to 3 decimal places

intercept=179.984.

slope=-0.076

The required equation is

Galloping speed Y=179.984-0.076 weight X

The required equation is  galloping speed Y = 179.984 - 0.076 weight X.

Given that,

Four-legged animals run with two different types of motion: trotting and galloping.

The number of strides per minute at which an animal breaks from a trot to a gallop depends on the weight of the animal.

We have to determine,

An equation that relates an animal's weight x (in pounds) and its lowest galloping speed y (in strides per minute).

According to the question,

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.

The required linear equation is,

y = a + bx

Where y is galloping speed and x is weight of animal.

To estimate intercept a and slope b from the table showing below.

x        y         x.y           x²

25     191.5   4787.5   625

35     184.7   6464.5  1225

50     175.8   8790     2500

75      162.2  12165     5625

500   124.9   62450  250000

1000  113.2   113200  1000000

Then,

sum of x = 1685 , sum of y = 952.3 , sum of xy = 207857 , sum of x² = 1259975.

Therefore, Slope of b is given by the formula;

[tex]b = \dfrac{(sum\ of \ xy )- (sumx).(sumy)}{n(sumx^{2})- (sumx)^{2} }\\\\b = \dfrac{6(207857)-1685(952.3)}{6(1259975)-(1685)^{2} }\\\\b = \dfrac{-357483.5}{4720625}\\\\b = -0.7573[/tex]

Then,

[tex]Y_b_a_r = \dfrac{sumx}{n} = \dfrac{952.3}{6} = 158.71\\\\X_b_a_r = \dfrac{sumy}{n} = \dfrac{1685}{6} = 280.83[/tex]

Therefore, The intercept is given by,

[tex]intercept = a = Y_b_a_r-b\times X_b_a_r\\\\intercept = a = 158.7167 - (-0.07573)\times 280.8333\\\\intercept = a = 158.7167 + 21.2675\\\\intercept = a = 179.984[/tex]

On rounding intercept and slope to 3 decimal places,

intercept = 179.984.

slope = -0.076

Hence, The required equation is  galloping speed Y = 179.984 - 0.076 weight X.

To know more about Linear equation click the link given below.

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Answer:

This question answer is attached in the attachment,

Step-by-step explanation:

Answer:

The probability that the mean diameter of the sample shafts would differ from the population mean by less than 0.2 inches is 0.5319.

Step-by-step explanation:

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

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

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

And the standard deviation of the distribution of sample mean is given by,

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

The information provided is:

[tex]\mu=200\\\sigma=22\\n=83[/tex]

Since n = 83 > 30, the Central Limit Theorem can be used to approximate the sampling distribution of sample mean diameter of the shafts.

Then:

Mean: [tex]\mu_{\bar x}=\mu=200[/tex]

Standard deviation: [tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{22}{\sqrt{83}}=2.415[/tex]

Compute the probability that the mean diameter of the sample shafts would differ from the population mean by less than 0.2 inches as follows:

[tex]P(\bar X-\mu_{\bar x}<0.20)=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}<\frac{0.20}{2.415})[/tex]

                            [tex]=P(Z<0.08)\\=0.53188\\\approx0.5319[/tex]

*Use a z-table.

Thus, the probability that the mean diameter of the sample shafts would differ from the population mean by less than 0.2 inches is 0.5319.

Answer:

4 taps take 70 minutes

2 taps would take 140 minutes

8 taps would take 35 minutes

time = (4 / # of taps) * 70

time = (4 / 7) * 70 = 40 minutes

Step-by-step explanation:

The height of the cylinder with a volume of 384π cubic inches and a radius of 8 inches is 6 inches.

To find the height of a cylinder with a known volume and radius, we use the formula for the volume of a cylinder, which is V =  πr²h, where 'V' is the volume, 'r' is the radius, and 'h' is the height. We are given a volume of 384π cubic inches and a radius of 8 inches. Plugging these values into the formula gives us:

384 π = π (8²) h
384 π = 64π h
h = 384 π ÷ 64π
h = 6 inches

Therefore, the height of the cylinder is 6 inches.

Answer:

50 cents or 0.5

Step-by-step explanation:

Answer:

9100

Step-by-step explanation:

I=Prt

I=7,000(.06)5

I=420(5)

I=2,100

2,100+7,000=9,100

5 times,I hoped this helped you out,if not sorry

Answer:

The risk consequence of both activities is 1.6 months.

Step-by-step explanation:

We can define a randome variable D: total delay time for the project, and calculate its expected value.

This would be the risk consequence of both activities.

The expected delay time for the project is the sum of the expected delay for task A plus the expected delay for task B. It is assumed the likelihood of a problem in any task is independent of the other.

Then, each expected delay for a task is equal to the probability of a problem multiplied by the consequence (delay time).

[tex]E(D)=E(D_a)+E(D_b)=p_aT_a+p_bT_b\\\\E(D)=0.5*2+0.2*3=1+0.6=1.6[/tex]

The risk consequence of both activities is 1.6 months.

Answer:

The 98% confidence interval for the average credit card balance is

(564.04, 635.96).

Step-by-step explanation:

We have to calculate the 98% confidence interval on the average credit card balance.

The sample will consist of the n=30 customers that have credit card.

The sample has a mean of $600 and a standard deviation of $80.

As the population standard deviation is estimated from the sample standard deviation, we will use a t statistic.

The degrees of freedom are:

[tex]df=n-1=30-1=29[/tex]

The critical value for a 98% CI and 29 degrees of freedom is t=2.463 (this can be looked up in a t-table).

Then, the margin of error is:

[tex]E=t\cdot s/\sqrt{n}=2.463*80/\sqrt{30}=197.04/5.48=35.96[/tex]

Then, the upper and lower bounds of the confidence interval are:

[tex]LL=\bar X-E=600-35.96=564.04\\\\UL=\bar X+E=600+35.96=635.96[/tex]

Answer:

[tex](0.08-0.0888) - 1.96 \sqrt{\frac{0.08(1-0.08)}{11545} +\frac{0.088(1-0.088)}{4691}}= -0.0175[/tex]  

[tex](0.08-0.0888) + 1.96 \sqrt{\frac{0.08(1-0.08)}{11545} +\frac{0.088(1-0.088)}{4691}}= 0.0015[/tex]  

And the 95% confidence interval would be given (-0.0175;0.0015).  

We are confident at 95% that the difference between the two proportions is between [tex]-0.0175 \leq p_A -p_B \leq 0.0015[/tex]

And since the confidence interval contains the 0 we have enough evidence to conclude that the population proportions are not significantly different at 5% of significance.

Step-by-step explanation:

Previous concepts

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

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

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

[tex]p_A[/tex] represent the real population proportion for California

[tex]\hat p_A =0.08[/tex] represent the estimated proportion for California

[tex]n_A=11545[/tex] is the sample size required for California

[tex]p_B[/tex] represent the real population proportion for Oregon

[tex]\hat p_B =0.088[/tex] represent the estimated proportion for Brand B

[tex]n_B=4691[/tex] is the sample size required for Oregon

[tex]z[/tex] represent the critical value for the margin of error  

Solution to the problem

The sample proportion have the following distribution  

[tex]\hat p \sim N(p,\sqrt{\frac{p(1-p)}{n}})[/tex]  

The confidence interval for the difference of two proportions would be given by this formula  

[tex](\hat p_A -\hat p_B) \pm z_{\alpha/2} \sqrt{\frac{\hat p_A(1-\hat p_A)}{n_A} +\frac{\hat p_B (1-\hat p_B)}{n_B}}[/tex]  

For the 95% confidence interval the value of [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2=0.025[/tex], with that value we can find the quantile required for the interval in the normal standard distribution.  

[tex]z_{\alpha/2}=1.96[/tex]  

And replacing into the confidence interval formula we got:  

[tex](0.08-0.0888) - 1.96 \sqrt{\frac{0.08(1-0.08)}{11545} +\frac{0.088(1-0.088)}{4691}}= -0.0175[/tex]  

[tex](0.08-0.0888) + 1.96 \sqrt{\frac{0.08(1-0.08)}{11545} +\frac{0.088(1-0.088)}{4691}}= 0.0015[/tex]  

And the 95% confidence interval would be given (-0.0175;0.0015).  

We are confident at 95% that the difference between the two proportions is between [tex]-0.0175 \leq p_A -p_B \leq 0.0015[/tex]

And since the confidence interval contains the 0 we have enough evidence to conclude that the population proportions are not significantly different at 5% of significance.