Plz help me well mark brainliest if correct!

Answer:

0.5188 = 51.88% probability of obtaining a difference between sample means of 110 mg or more

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution, the central limit theorem and difference between normal variables.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Subtraction of normal sample means:

When we subtract two distribution of the sample means, which are normal, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of standard errors squared.

Sample size of 55 men with mean 785 and standard deviation 489

This means that:

[tex]\mu_A = 785[/tex]

[tex]s_A = \frac{489}{\sqrt{55}} = 65.9367[/tex]

Sample size of 40 women with mean 670 and standard deviation of 419

This means that:

[tex]\mu_B = 670[/tex]

[tex]s_B = \frac{419}{\sqrt{40}} = 66.2497[/tex]

Difference between sample means:

The mean and the standard deviation are, respectively:

[tex]\mu = \mu_A - \mu_B = 785 - 670 = 115[/tex]

[tex]\sigma = \sqrt{s_A^2+s_B^2} = \sqrt{65.9367^2+66.2497^2} = 93.47[/tex]

What is the probability of obtaining a difference between sample means of 110 mg or more?

This is 1 subtracted by the pvalue of Z when X = 110. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{110 - 115}{93.47}[/tex]

[tex]Z = -0.053[/tex]

[tex]Z = -0.053[/tex] has a pvalue of 0.4812.

1 - 0.4812 = 0.5188

0.5188 = 51.88% probability of obtaining a difference between sample means of 110 mg or more

Answer:

c = 8.4m is the answer.

Step-by-step explanation:

a = 6m

b = 6m

c = ?

According to the Pythagorean theorem,

a² + b² = c²

6² + 6² = c²

36 + 36 = c²

c² = 72

c = 8.4m

∴ The mouse runs 8.4 m from the opposite corners of the room.

Answer:

8.5 m

Step-by-step explanation:

If you draw the segment from one corner to the opposite corner, you'll have the hypotenuse of a triangle with two legs of 6 m. We can find the length of the hypotenuse using the Pythagorean Theorem.

a^2 + b^2 = c^2

6^2 + 6^2 = c^2

36 + 36 = c^2

c^2 = 72

c = sqrt(72)

c = 6sqrt(2) = 8.5

Answer: 8.5 m

Answer:

0.64%.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 75 grams and a standard deviation of 22 grams.

This means that [tex]\mu = 75, \sigma = 22[/tex]

Sample of 144:

This means that [tex]n = 144, s = \frac{22}{\sqrt{144}} = 1.8333[/tex]

More than 80 or less than 70:

Both are the same distance from the mean, so we find one probability and multiply by 2.

The probability that it is less than 70 is the pvalue of Z when X = 70. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{70 - 75}{1.8333}[/tex]

[tex]Z = -2.73[/tex]

[tex]Z = -2.73[/tex] has a pvalue of 0.0032

2*0.0032 = 0.0064.

0.0064*100% = 0.64%

The probability is 0.64%.

Answer:

aa

Step-by-step explanation:

aaaaaaaaa i need points sorry

9514 1404 393

Answer:

  $4047

Step-by-step explanation:

For an interest rate r compounded n times per year for t years, the effective multiplier is ...

  (1 +r/n)^(nt)

The multiplier for the first 5 years is ...

  (1 +0.07/2)^(2·5) = 1.41059876

The multiplier for the last 5 years is ...

  (1 +0.0728/4)^(4·5) = 1.43437218

Then the account value at the end of 10 years is ...

  $2000(1.41059876)(1.43437218) ≈ $4047 . . . . balance after 10 years

Answer:

smallest: 1059

largest: 9510

Answer:

Step-by-step explana

Answer:

Step-by-step explanation:

What is the answer

Answer:

(18.1361 ; 19.5639) ;

using a smaller sample will widen the margin

Step-by-step explanation:

Given :

Xbar = 18.85

Standard deviation, s = 1.75

Sample size, n = 40

Confidence interval is obtained using the relation :

Xbar ± Margin of error

Margin of Error = Zcritical * s/ √n

Zcritical at 99% = 2.58

Margin of error = 2.58 * (1.75/√40) = 0.7139

Lower boundary = 18.85 - 0.7139 = 18.1361

Upper boundary = 18.85 + 0.7139 = 19.5639

(18.1361 ; 19.5639)

B.)

The sample size, n being the denominator in the margin error formula increases the error value as it reduces or decreases in value Hence widens the interval. Conversely, increasing the sample size reduces the error margin value and ultimately narrows the interval.

Therefore, using a smaller sample will widen the margin

Answer:

170 in^2

Step-by-step explanation:

you have to find the area of each surface of the square

1) the square on the right side:

5x5=25 in^2

there are 2 of these on opposite sides

2)the of the rectangle facing us;

6x5=30in^2  (5 because 5 is the height)

there are 4 of these

3)add up all the areas

25+25+30+30+30+30=170in^2

9514 1404 393

Answer:

  y = 6

Step-by-step explanation:

Let's call the marked angles A, B, C, clockwise from upper left.

Along the vertical transversal, we observe that A+90° and C are alternate exterior angles, so are congruent. This lets us find a value for x.

  A+90 = C

  4x +90 = 11x -8

  98 = 7x

  14 = x

Then angle A is ...

  A = 4x° = 4(14)° = 56°

__

Along the horizontal transversal, we observe that A and B are alternate exterior angles, so are congruent. This lets us find a value for y.

  A = B

  56° = (9y +2)°

  54 = 9y

  6 = y

The value of y is 6.

Answer:

56

Step-by-step explanation:

type in calculator 7*((2+8)-2)

Answer: Angle VUW and QRP are alternate exterior angles.

They are both exterior and are on alternate sides of the transversal.

Hope this helps!

Answer:

4 /1 5 also 0.26666666666

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Answer:

The 95% confidence interval for the difference in mean profile height and mean actual height of online daters is between 0.27 and 0.87 inches.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 30 - 1 = 29

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 29 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.0452

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.0452\frac{0.81}{\sqrt{30}} = 0.3[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 0.57 - 0.3 = 0.27 inches.

The upper end of the interval is the sample mean added to M. So it is 0.57 + 0.3 = 0.87 inches.

The 95% confidence interval for the difference in mean profile height and mean actual height of online daters is between 0.27 and 0.87 inches.

Answer:

A is bethel

B is below sea level by 22 feet

C is I would describe the elevation very low  lowest elevation in North America

D is 0 the elevation is right at sea level.

E is  has a lower elevation and is one of the lowest major cities in the entire United States.

Step-by-step explanation:

Answer:

1.True

2.False

3.False

Step-by-step explanation:

1. b is less down the number line than a

2. a is more down the number line and the positive version is higher

3. positive is bigger than negative

Answer:

9

Step-by-step explanation:

To solve this question you need the formula of hypothenuse theorem, I personally use [tex]a^{2} + b^{2} = c^{2}[/tex].

Since [tex]c^{2}[/tex] is the hypothenuse, and the hypothenuse in this case is 15, the equation will be [tex]12^{2}+ b^{2} = 15^{2}[/tex].

144+[tex]b^{2}[/tex]=225

subtract 144 from both sides

[tex]b^{2}[/tex]= 81

[tex]\sqrt{b^{} } = \sqrt{81}[/tex]

b=9

Answer:

Answer is 51

Step-by-step explanation:

5(6) + 3(7)

30 + 21

51

Answer:

first you woub sub 6 into x and 7 into y then you would multiple 5 and 6 to get 30 and then multiple 3 and 7 to get 21. lastly add 30 and 21 to give a total of 51

Step-by-step explanation:

5x+3y

5(6)+3(7)

30+21

51

hope this helps

Answer:

5 and 48

Step-by-step explanation:

27:45

Simplify the ratio

3:5

The first one must be 5, and option 1 (5 and 48) is the only one with 5.

Answer:

Step-by-step explanation:

Equation

Let "n" represent the number. Then more indicates addition, and times indicates multiplication. With that said, the answer is 4 + 3n.

Dale's Money

Given: $44 in total

44 ÷ 2 (To know how much they have  equally)

22

22 ÷ 3 (Then you divide by 3 because Brandon has 3 times his, the opposite of multiplication is division.)

7.3

Therefore, Dale has $7.3¢

Brandon's money

Given: 4 + 3n. Dale has 7.3

Solve: 7.3 × 3 ( Since Brandon has four more than 3 times the amount of money that Dale has, multiply that and 3)

21.9 (Then add four because Brandon has four more...)

25.9

Therefore, Brandon has $25.9¢

The amount that Brandon and Dale have is $34 and $10, respectively.

An equation is formed when two expressions are equated with each other with the help of an equal sign.

Let the amount of money that Brandon has be x, and Dale has be y.

As it is given that the sum of the total amount they both had is $44. therefore, the equation that can represent the total amount both of them had is

[tex]x + y = \$44[/tex]

Now, according to the first statement, Brandon has four more than 3 times the amount of money that Dale has. therefore, the equation can be represented as,

[tex]x = 4 + 3y[/tex]

Further, as got the two-equation solving the two equations. We have the value of x, therefore, substitute the value of x in the first equation,

[tex]x+y = 44\\\\(4 + 3y )+y= 44\\\\4+4y=44\\\\4y = 40\\\\y = 10[/tex]

Now, substitute the value of y in the second equation we get,

[tex]x = 4 + 3y\\\\x = 4 + 3(10)\\\\x = 34[/tex]

Hence, The amount that Brandon and Dale have is $34 and $10, respectively.

Learn more about Equation:

https://brainly.com/question/24944275

Answer:

[tex]\angle 1 \cong \angle 7[/tex]

Step-by-step explanation:

We proceed to present which angles corresponds with [tex]\angle 7[/tex], accompained with reason based on Theorems used in Euclidean Geometry. Two angles are correspondent if and only if are in the same side of the secant line, one of them is internal and the other one is external.

Hence, we conclude that [tex]\angle 1 \cong \angle 7[/tex].

Answer:

14

Step-by-step explanation:

Hope this Helps!!!!!

The area of the sector is  76. 95 m

Using the formula;

Area of  sector of a circle  = /360° (r2)

where r is the radius of the circle

is the angle of the sector

From the diagram,

= 77°

r = 10. 7m

= 3. 142

Substitute into the formula

Area of the sector = 77/ 360° * (3. 142* 10. 7 * 10. 7)

Area of the sector = 0. 2139 * 359. 72

Area of the sector = 76. 95 m

Thus, the area of the sector is  76. 95 m

Learn more about the area of a sector here:

https://brainly.com/question/22972014

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Answer:

The investment will generate $ 60 in interest, with which the new balance will be $ 1060.

Step-by-step explanation:

To determine how much interest would $ 1,000 earn in one year at a rate of 6%, compounded annually, and what would be the new balance, the following calculations must be performed:

1000 x (1 + 0.06 / 1) ^ 1x1 = X

1000 x 1.06 ^ 1 = X

1000 x 1.06 = X

1060 = X

Therefore, the investment will generate $ 60 in interest, with which the new balance will be $ 1060.

Answer:

1507.96

Step-by-step explanation:

Answer:

I would use the sale price.

Step-by-step explanation:

20% of 150 is 30. So, you get $30 off if you use the sale price rather then the $15 coupon.

Answer:

Diagonal = 13 yd

Step-by-step explanation:

The diagonal of the 3D shape can be solved using the extension of the pythagorean theorem, which is given as: d² = a² + b² + c²

Where,

a = 12 yd

b = 3 yd

c = 4 yd

d = diagonal

Plug in the values

d² = 12² + 3² + 4²

d² = 169

d = √169

d = 13 yd