Carl's taxable income is $36,064. He is filing as married filing jointly, and he has already paid $4110 in federal taxes.

What will he receive or pay after he figures his taxes for the year?
A. He will receive a refund of $431.
B. He will pay $431.
C. He will receive a refund of $424.
D. He will pay $424.

(a) The probability of observing exactly 11 heads is 0.1020.

(b) The probability of observing exactly 12 heads is 0.0687.

(c) The cumulative probability of observing 12 or fewer heads is 0.9531.

a. To calculate the probability of observing exactly 11 heads in 30 flips, we can use the binomial distribution with parameters n = 30 (number of flips) and p = 0.50 (proportion of heads):

P(X = 11) = (30 choose 11) * (0.50)^11 * (1 - 0.50)^(30 - 11)

P(X = 11) = 0.1020 (rounded to four decimal places)

Therefore, the probability of observing exactly 11 heads is 0.1020.

b. To calculate the probability of observing exactly 12 heads in 30 flips, we can use the same formula:

P(X = 12) = (30 choose 12) * (0.50)^12 * (1 - 0.50)^(30 - 12)

P(X = 12) = 0.0687 (rounded to four decimal places)

Therefore, the probability of observing exactly 12 heads is 0.0687.

c. To calculate the cumulative probability of observing 12 or fewer heads (a sample proportion of 0.4 or lower), we can sum the probabilities of observing 0, 1, 2, ..., 12 heads:

P(X <= 12) = P(X = 0) + P(X = 1) + ... + P(X = 12)

We can use software or a binomial probability table to calculate these probabilities and then sum them up. Alternatively, we can use the complement rule and subtract the probability of observing 13 or more heads from 1:

P(X <= 12) = 1 - P(X >= 13)

P(X <= 12) = 1 - [P(X = 13) + P(X = 14) + ... + P(X = 30)]

Using a binomial probability table or software, we can find that:

P(X >= 13) = 0.0469 (rounded to four decimal places)

Therefore,

P(X <= 12) = 1 - P(X >= 13) = 1 - 0.0469 = 0.9531

So the cumulative probability of observing 12 or fewer heads is 0.9531.

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Answer:

$525

Step-by-step explanation:

Jackie starts with $500, and the interest rate is 5% per year.

This means that, after one year, Jackie will have accumulated 5% interest with the $500 she put into the savings account.

Now, we can find 5% of $500 by converting 5% to its fraction form, which is 5/100. 5% of a value means that you need to multiply the fraction (or decimal) by the said value. So, we have:

[tex]\frac{5}{100}[/tex] · 500 =

[tex]\frac{2500}{100}[/tex] =

25

Therefore, the amount of interest she has accumulated in one year is $25. Combined with the money in her savings account, she has $525, since $500 + $25 = $525.

The power of a statistical test of hypotheses is the probability that the test will reject the null hypothesis when a particular alternative value of the parameter is true.

It is the ability of the statistical test to detect a true difference between groups, or a true relationship between variables, when it exists. A high power indicates that the test has a low probability of making a type II error (failing to reject a false null hypothesis).

The power of a test is affected by various factors such as the sample size, level of significance, effect size, and variability of the data.

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It is not equal to 1 - (P-value), nor is it the smallest significance level at which the data will allow you to reject the null hypothesis or the probability that the test will reject both one-sided and two-sided hypotheses.

The correct answer is: The power of a statistical test of hypotheses is the probability that a significance test will reject the null hypothesis when a particular alternative value of the parameter is true. It is the ability of the test to detect a true difference or effect between two groups or conditions. The power is influenced by factors such as the sample size, effect size, and significance level, and is usually calculated before conducting a study to ensure that it has sufficient power to detect meaningful differences. It is not equal to 1 - (P-value), nor is it the smallest significance level at which the data will allow you to reject the null hypothesis or the probability that the test will reject both one-sided and two-sided hypotheses.

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The probability that the dog is still lost at the end of the second day is 0.41

To solve this problem, we can use Bayes' theorem, which allows us to update the probability of an event based on new information.

Let A be the event that the dog is in forest A, and B be the event that the dog is in forest B. Let F be the event that the dog is found within two days.

We want to calculate P(F'), the probability that the dog is still lost at the end of the second day. We can use the law of total probability to express this as

P(F') = P(F'|A) × P(A) + P(F'|B) × P(B)

where P(F'|A) is the probability of not finding the dog within two days given that the dog is in forest A, P(F'|B) is the probability of not finding the dog within two days given that the dog is in forest B, and P(A) and P(B) are the prior probabilities of the dog being in forest A and forest B, respectively.

Using the information given in the problem, we can calculate

P(F'|A) = 1 - 0.5 = 0.5 (the probability of not finding the dog in forest A within two days is 1 - 0.5 = 0.5)

P(F'|B) = 1 - 0.8 = 0.2 (the probability of not finding the dog in forest B within two days is 1 - 0.8 = 0.2)

P(A) = 0.7 (the prior probability of the dog being in forest A)

P(B) = 0.3 (the prior probability of the dog being in forest B)

Plugging these values into the formula above, we get

P(F') = 0.5 × 0.7 + 0.2 × 0.3 = 0.41

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The given question is incomplete, the complete question is:

Oscar has lost his dog; there is a 70% probability it is in forest A and a 30% chance it is forest B. If the dog is in forest A and Oscar looks there for a day, he has a 50% change of finding the dog. If the dog is in forest B and Oscar looks there for a day, he has an 80% chance of finding the dog. what is the probability that the dog is still lost at the end of the second day?

Step-by-step explanation:

There is an equal number of protons and electrons.... they balance each other so that the net charge is zero.

In the given problem, the surface area of the triangular prism is 65 square centimeters. The answer is not listed among the options provided

We need to find the surface area of the triangular prism, which is the sum of the areas of all its faces.

The triangular faces of the prism are congruent triangles, so we can find their area by multiplying the base and height and dividing by 2. The dimensions of the triangular faces are 5 cm (base) and 4 cm (height).

Area of each triangular face = (5 cm x 4 cm)/2 = 10 cm²

The rectangular faces are congruent rectangles, so we can find their area by multiplying the length and width. The dimensions of the rectangular faces are 5 cm x 3 cm and 3 cm x 4 cm.

Area of each rectangular face = (5 cm x 3 cm) = 15 cm²

Total surface area of the prism = 2 x Area of triangular face + 3 x Area of rectangular face

= 2 x 10 cm² + 3 x 15 cm²

= 20 cm² + 45 cm²

= 65 cm²

Therefore, the surface area of the triangular prism is 65 square centimeters. The answer is not listed among the options provided, so there might be a mistake in the question or answer choices.

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The greatest number of songs downloaded is 10."

"What is the greatest number of songs downloaded?" is:

A dot plot is a graphical representation of data using dots. In this case, the dot plot shows the number of songs Carly downloaded over 15 successive weekends. Each dot represents the number of songs downloaded during a particular weekend

To find the greatest number of songs downloaded, we need to identify the highest point on the dot plot. This can be done by visually examining the dot plot and looking for the highest dot.

Once we identify the highest dot, we can see the number of songs downloaded during that particular weekend, which is the greatest number of songs downloaded over the 15 successive weekends.

if the highest dot on the dot plot represents 10 songs downloaded, then the answer to the question would be "The greatest number of songs downloaded is 10."

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The number of volunteers who worked more than 15 hours can be found by summing up the frequencies

of the bars in the histogram that represent the groups with more than 15 hours of community service.

To determine how many volunteers worked more than 15 hours using the given histogram.

Identify the section of the histogram that represents volunteers who worked more than 15 hours.

Read the height (frequency) of the bars representing the groups of volunteers with more than 15 hours of community

service.

Add the frequencies of these bars to get the total number of volunteers who worked more than 15 hours.

In conclusion, the number of volunteers who worked more than 15 hours can be found by summing up the frequencies

of the bars in the histogram that represent the groups with more than 15 hours of community service.

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Answer: 10

Step-by-step explanation:

10

If the researcher performed an ANOVA test and rejected the null hypothesis, it indicates that there is a significant difference between at least two group means.

To determine which specific groups differ significantly, post hoc tests are performed. If there are five levels of the independent variable, there are ten possible pairwise comparisons that can be made (5 choose 2).

Therefore, the researcher would make 10 post hoc comparisons. These tests would identify which specific groups differ significantly and would help the researcher draw more precise conclusions about the relationship between the independent variable and the dependent variable.

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Some possible prices for the socks that would meet this condition are $2.99, $2.50, $3.00, $2.95, etc.

A rate is a measure of the amount of change of one quantity with respect to another quantity. It expresses how much one quantity changes in relation to another quantity over a given time or distance.

If Diego has budgeted $35 for 5 pairs of socks and a pair of shorts, we can subtract the cost of the shorts from the total budget to find the amount he has left for the socks:

$35 - $19.95 = $15.05

To find the possible prices for the socks, we can divide the amount Diego has left by the number of pairs of socks he needs:

$15.05 / 5 pairs = $3.01 per pair

Therefore, Diego would be able to stay within his budget if he finds socks that cost $3.01 or less per pair. Some possible prices for the socks that would meet this condition are $2.99, $2.50, $3.00, $2.95, etc.

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Answer:

the x-coordinate and y-coordinate change places.

Step-by-step explanation: so you reflect a point across the line y = x, the x-coordinate and y-coordinate change places. If you reflect over the line y = -x, the x-coordinate and y-coordinate change places and are negated (the signs are changed). the line y = x is the point (y, x). the line y = -x is the point (-y, -x).

The missing angles in the given pair of lines AB and CD with transversals EF & GH intersecting at O & missing sides on the basis of similarity of triangles are:

∠IKF=w°=109°

JO=z=2.7 units

∠JLO=x°=39°

∠DLO=y°=141°

What is similarity?

If two forms or figures have an equal number of comparable sides and angles, they are said to be similar. Similar figures are those when two or more figures share the same shape but have varied sizes.

Given that

∠KIO=39°

∠IKO=71°

∠IOK=70°

IO=12 units

KO=8 units

LO=4 units

a)We know that ∠KIO=∠OLJ  {alternate interior angles}

∠KIO=∠OLJ=39°

∴x° = 39°

b)We know that ∠OLJ+∠OLD=180° {linear pair}

x°+y°=180°

39°+y°=180°

y°=180-39

y°=141°

c)We know that ∠IKO+∠IKF=180° {angles on straight line}

71°+w°=180°

w°=180-71

w°=109°

d)In ΔOKI and ΔOJL, we can see that

∠OIK=∠OLJ=39°

∠OKI=∠OJL=71°

∠KOI=∠JOL=70°

as the angles are congruent, we can say that ΔOKI and ΔOJL are similar.

∴Sides will be in same ratio

[tex]\frac{OI}{OL}[/tex]  = [tex]\frac{OK}{OJ}[/tex]  = [tex]\frac{KI}{JL}[/tex]

Taking [tex]\frac{OI}{OL}[/tex]  = [tex]\frac{OK}{OJ}[/tex]

[tex]\frac{12}{4} = \frac{8}{z}[/tex]

3z = 8

z =2.667

z≈2.7 units

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Answer: To find the point on the line 3x + y = 8 that is closest to the point (-3,2), we need to minimize the distance between the line and the point.

Let (x, y) be the point on the line that is closest to (-3, 2). Then the vector from the point (-3, 2) to (x, y) is orthogonal (perpendicular) to the line. The direction vector of the line is <3, 1>, so the direction vector of the orthogonal vector is <-1/3, 1>.

Now we can write an equation for the line passing through (-3, 2) with the direction vector <-1/3, 1>:

(x - (-3))/(-1/3) = (y - 2)/1

Simplifying, we get:

3x + y = 11

This is the line passing through (-3, 2) that is orthogonal to the original line 3x + y = 8.

To find the intersection of these two lines, we can solve the system of equations:

3x + y = 8

3x + y = 11

Subtracting the first equation from the second, we get:

0 = 3

This is a contradiction, which means the two lines do not intersect. Therefore, the point on the line 3x + y = 8 that is closest to (-3, 2) does not exist.

However, we can still find the closest point to (-3, 2) on the line 3x + y = 8. This point will be the intersection of the line passing through (-3, 2) with the direction vector <-1/3, 1> and the line 3x + y = 8.

The equation of the line passing through (-3, 2) with the direction vector <-1/3, 1> is:

(x - (-3))/(-1/3) = (y - 2)/1

Simplifying, we get:

3x + y = 11

To find the intersection point with the line 3x + y = 8, we can solve the system of equations:

3x + y = 8

3x + y = 11

Subtracting the first equation from the second, we get:

0 = 3

This is a contradiction, which means the two lines do not intersect. Therefore, the point on the line 3x + y = 8 that is closest to (-3, 2) does not exist.

Step-by-step explanation:

The classification for a score of 73 on an IQ test with a mean of 100 and standard deviation of 15 is "below average".

For intelligence level tests with a mean of 100 and a standard deviation of 15, a score of 73 would address a characterization of less than ideal knowledge.

To comprehend this order, it is vital to realize that level of intelligence scores are normalized, meaning they depend on a dispersion where the typical score is 100 and the standard deviation is 15. This dissemination is frequently alluded to as a typical circulation, with most of scores falling inside one standard deviation of the mean.

A score of 73 is one and a half standard deviations underneath the mean (100-15-15=70). This places it in the seventh percentile, meaning just 7% of the populace would score lower.

As indicated by most intelligence level grouping frameworks, a score of 73 would fall inside the scope of marginal scholarly working or low normal knowledge. It is essential to note, nonetheless, that intelligence level scores are only one proportion of knowledge and ought not be utilized in segregation to decide an individual's scholarly capacities.

In outline, a score of 73 on a level of intelligence test with a mean of 100 and a standard deviation of 15 would address sub optimal knowledge and fall inside the scope of marginal scholarly working or low normal insight.

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Answer:

Step-by-step explanation:

domain is -infinity to positive infinity range is -3 to infinity. Increasing from -3 to infinity and decreasing from - infinity to -3 and it’s minimum

The main topic is the split-half reliability test used in psychological research to assess the internal consistency of a scale.

In psychological research, reliability is a crucial aspect of measuring constructs or attributes. One commonly used method for assessing the reliability of a scale is the split-half reliability test.

In this test, the scale questions are divided into two parts equally, and the resulting scores of both parts are correlated against one another.

For example, if a scale had 20 items, the items could be randomly split into two groups of 10 items each.

Scores are then calculated for each group, and the scores are correlated with each other to determine the degree of consistency between the two halves.

The correlation coefficient obtained from this analysis provides an estimate of the internal consistency of the scale.

A high correlation coefficient indicates a high level of internal consistency, indicating that the two halves of the scale are measuring the same construct or attribute.

Conversely, a low correlation coefficient suggests that the two halves of the scale are not measuring the same construct or attribute, and the scale may need to be revised or abandoned.

Overall, the split-half reliability test provides a quick and efficient method for evaluating the reliability of a scale.

However, it is important to note that this method does have some limitations, such as the possibility of unequal difficulty or discrimination of the items in each half of the scale.

Therefore, researchers often use other methods, such as Cronbach's alpha, in conjunction with the split-half reliability test to provide a more comprehensive assessment of the reliability of a scale

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Answer: 4,500 i got this answer

:)

Step-by-step explanation:

Answer:

Step-by-step explanation:

1.8million/400

[tex]18 * 10 ^{-1} *10^{6}*10^{-2} /4[/tex]

=4.5*10^3

=4.5*1000

=4500

Answer: the same

Step-by-step explanation:

because it says they practice as many hours as you do

Answer:

.40n = 80, so n = 200

.95 × 200 = 190

Answer:

190

Step-by-step explanation:

The average size of a customer's bill at a restaurant that earns daily $3,250 for the meals that it sells to 200 customers is $16.25. Therefore, the right answer is option (c).

The average or mean is calculated by taking the ratio of the total sum of the outcomes of an event to the frequency or the number of times the event occurs.

It can be written as [tex]\frac{n_1+n_2+.....+n_a}{a}[/tex].

In the given question, the sum of the customer bill is given as $3,250.

And the number of customers served is given to be 200.

Therefore, the average size of a customer's bill is calculated by [tex]\frac{3250}{200}[/tex]

Which turns out to be $16.25.

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The answer is $16.25. To find the average size of a customer's bill, you would divide the total earnings by the number of customers.
$3,250 / 200 customers = $16.25 per customer.

To find the average size of a customer's bill at the restaurant, you need to divide the total daily earnings by the number of customers. Here's a step-by-step explanation:

1. The restaurant earns $3,250 daily from the meals it sells.
2. The restaurant serves 200 customers daily.

Now, calculate the average bill size:

3. Divide the total daily earnings ($3,250) by the number of customers (200).

$3,250 ÷ 200 = $16.25

The average size of a customer's bill at the restaurant is $16.25.

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The calculated value of the length of the segment EG is 54 units.

Since J is the midpoint of EG, we know that EJ = JG.

So, we can set the two expressions equal to each other and solve for x:

5x - 3 = 3x + 9

Subtracting 3x from both sides, we get:

2x - 3 = 9

Adding 3 to both sides, we get:

2x = 12

Dividing both sides by 2, we get:

x = 6

Now that we have x, we can substitute it back into either EJ or JG to find its value:

EJ = 5x - 3 = 5(6) - 3 = 27

JG = 3x + 9 = 3(6) + 9 = 27

Therefore, EG = EJ + JG = 27 + 27 = 54.

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a) Positive correlation, b) No correlation, c) Negative correlation

a) Positive correlation - as the hours of lacrosse practice increase, the number of goals scored in a lacrosse game is likely to increase as well.

b) No correlation - there is no obvious relationship between a student's average marks and the number of siblings in their family.

c) Negative correlation - as the distance from a student's home to their school increases, the time they spend on the school bus each day is likely to decrease.

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As per the given question, based on performance and z-scores, Barney scored better than Fred.

To determine who scored better between Fred and Barney, it is required to compare their scores with respect to rest of the class. This can be done by calculating their z-scores.

Determining the score for Fred:

z-score = (x - μ) / σ

= (71 - 81) / 5

= -10/5

= -2

Determining the score for Barney:

z-score = (x - μ) / σ

= (84 - 95) / 8

= -11/8

= -1.375

Both z-scores are negative because both scores fall below the means of their respective classes. Although Barney's z-score of -1.375 is closer to the mean than Fred's z-score of -2.

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Step-by-step explanation:

Given :

Circumstance = 176 mm

We know that,

C = 2πr

r = C / 2π

r = 176 × 7/ 22 × 2

r = 1232/44

r = 28 mm

Now,

d = 2r = 2(28) = 56 mm

Now,

A = π r²

A = 22/7 × (28)²

A = 22/7 × 784

A = 17248/7

A = 2464 mm²

Answer:

Step-by-step explanation:

Circumference, C = 2πr

given: c=176mm, π=[tex]\frac{22}{7}[/tex]

c = 2 x [tex]\frac{22}{7}[/tex] x r

176 = [tex]\frac{44}{7}[/tex]r

r = [tex]\frac{7 *176}{44}[/tex]

r = 28

Area, A = π[tex]r^{2}[/tex]

A = [tex]\frac{22}{7}[/tex] x [tex]28^{2}[/tex]

A = 2464[tex]mm^{2}[/tex]

Answer: The angle between line AB and the axis of the cylinder is 60 degrees.

Step-by-step explanation:

Let's draw a cross-sectional diagram of the cylinder to help visualize the problem.

Label the center of the top circle as O and the center of the bottom circle as O'.

Label the midpoint of line AB as M.

Draw a line from M to the center of the cylinder, which intersects the axis of the cylinder at point C.

Because line AB is perpendicular to the axis of the cylinder, line MC is also perpendicular to line AB.

Label the length of line MC as h, and the distance between point M and the axis of the cylinder as x.

By the Pythagorean theorem, we know that OM^2 + h^2 = R^2 (the radius of the cylinder)

Similarly, O'M^2 + h^2 = R^2

Subtracting these two equations, we get OM^2 - O'M^2 = 0, which means that OM = O'M = R.

Therefore, triangle MOC is an isosceles triangle with MO and O'M both equal to R.

Because x is the distance between line AB and the axis of the cylinder, we know that x = MC - (R√3)÷2.

We also know that h = R - x (because OM = R).

Using the Pythagorean theorem, we can solve for MC: (R^2 - h^2)^0.5 = MC

Substituting h = R - x, we get MC = (2Rx - x^2)^0.5

Setting MC = (R√3)÷2 (from the problem statement), we can solve for x: x = R(3 - 3^0.5)^0.5

Finally, using the tangent function, we can solve for the angle between line AB and the axis of the cylinder: tanθ = (R√3)÷2 / x, where θ is the angle we are looking for.

Substituting x from step 15, we get tanθ = 1 / (3 - 3^0.5)

Using a calculator, we can solve for θ: θ = 60 degrees.

The number of poetry books at the library that are for children is 510

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

Books = 600

If 8.5/10 of the poetry books are for children, we can calculate the number of poetry books for children as follows:

Number of poetry books for children = (8.5/10) x 600

Number of poetry books for children = 510

Therefore, there are 510 poetry books at the library for children.

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The functions 7 are inverse functions while the functions 8 are not inverse functions

To verify that f and g are inverse functions, we need to show that:

Let's apply these conditions to the given functions:

f(x) = 5x + 2; g(x) = (x−2)/5

f(g(x)) = f((x−2)/5) = 5((x−2)/5) + 2 = x − 2 + 2 = x

g(f(x)) = g(5x + 2) = ((5x + 2) − 2)/5 = 5x/5 = x

Since f(g(x)) = x and g(f(x)) = x, we can conclude that f and g are inverse functions.

f(x) = ½x − 7; g(x) = 2x + 14

f(g(x)) = f(2x + 14) = ½(2x + 14) − 7 = x

g(f(x)) = g(½x − 7) = 2(½x − 7) + 14 = x − 7 + 14 = x + 7

Since f(g(x)) = x and g(f(x)) ≠ x, we can conclude that f and g are not inverse functions.

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The given expression in the form ax + b will be (B) 1.8x + 4.1.

A finite collection of symbols that are properly created in line with context-dependent criteria is referred to as an expression, sometimes known as a mathematical expression.

An example is the expression x + y, which combines the terms x and y with an addition operator.

In mathematics, there are two different types of expressions: algebraic expressions, which also include variables, and numerical expressions, which solely comprise numbers.

So, we have the expression:

(3.6x-1.4) - (1.8x-5.5)

First, solve it in the form of ax + b as follows:

(3.6x-1.4) - (1.8x-5.5)

3.6x-1.4 - 1.8x+5.5

1.8x + 4.1

So, we have the expression: 1.8x + 4.1

Then, the coefficient and content will be (B) and the correct expression would be 1.8x + 4.1.

Therefore, the given expression in the form ax + b will be (B) 1.8x + 4.1.

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The probability of picking a male from the population whose weight will be greater than 251 lbs is 0.13%.

In order to calculate the probability we need to use the formula of z-score

z = (x -μ)/ σ

here,

x = value of interest

μ = population mean

σ = population standard deviation

now adding the values into the given formula

z = ( 251 -182)/23

z =  69/23

z = 3

now after using the standard distribution table the probability of a z-score greater than 3 is 0.13%

The probability of picking a male from the population whose weight will be greater than 251 lbs is 0.13%.

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