3. We will now study probability distributions that can be obtained from the data. (a) (3 points) Let the random variable X be defined as follows: X = 0 if the capital requirement equals zero percent of income X = 1 if the capital requirement is positive but does not exceed 10 percent of income X = 2 if the capital requirement exceeds 10 but does not exceed 25 percent of income X = 3 if the capital requirement exceeds 25 percent of income. Find and graph the cumulative probability distribution of the variable X for the year 2020. (b) (2 points) Using the distribution from exercise 3(a), compute P(1 ≤ X < 3). (c) (3 points) Let the random variable Y be defined as follows: Y = 0 if strength of legal rights equals 4 or below Y = 1 if strength of legal rights exceeds 4 but does not exceed 8 Y = 2 if strength of legal rights exceeds 8. Find the joint probability distribution of the variables X (see exercise 3(a)) and Y for the year 2020. (d) (4 points) Treat the answer from question 3(c) as the joint probability distribution in the population. Using that distribution, what is the correlation between X and Y ?

The equation −6x + 4 = -4 has x = 8 as its only solution, which can be verified using the substitution property of equality.

The equation that has x = 8 as its only solution is − (6x + 4) = 2x − 4. To solve this equation, we first need to move all the terms with x to one side and all the constants to the other side. To do this, we can first subtract 2x from both sides, giving us −6x − 4 = −4. We then need to subtract 4 from both sides, giving us −6x = −8. Finally, we need to divide both sides by −6 to get x = 8.

To check if this is the only solution, we can use the substitution property of equality. This property states that if two expressions are equal, then replacing one with the other should still make the equation equal. Therefore, if we substitute x = 8 into the original equation, we should get 0 = 0. To do this, we plug 8 into the equation and get − (6(8) + 4) = 2(8) − 4, which simplifies to −52 = 8 − 4, which is equal to 0 = 0. Since the equation still holds true, x = 8 is the only solution.

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a) The probability of a randomly selected diner waits less than 8 minutes for a table is 0.4

b) The probability of a randomly selected diner waits more than 1.5 minutes is 0.925

Given, wait times of between 0 and 20 minutes at a local restaurant follow a uniform distribution.

The probability density function of a uniform distribution is given by

f(x) = {1/(b-a)} where a ≤ x ≤ b

where a = 0 and b = 20

Therefore, the probability density function of f(x) = 1/20 for 0 ≤ x ≤ 20

For the  probability that a randomly selected diner waits between 2 and 7.5 minutes for a table, we need to find the area under the curve from x = 2 to x = 7.5

∴ P(2 ≤ x ≤ 7.5) = ∫₂⁷.⁵(1/20) dx

= 5.5/20 ⇒ 0.275

a) We need to find the area under the curve from x = 0 to x = 8

∴ P(x < 8) = ∫₀⁸(1/20) dx

= 8/20 ⇒ 0.4

b) We need to find the area under the curve from x = 1.5 to x = 20

∴ P(x > 1.5) = ∫₁.₅²⁰(1/20) dx

= 18.5/20 ⇒ 0.925

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α = 0.1

Answer: (a) Suppose X ∼ Bin(n, p). The likelihood function isL(p) = [n!/x!(n − x)!] px (n−p)−x.Then, we get the likelihood ratio asLR = [L(p1)] / [L(p0)]=[p1^x * (1−p1)^(n−x)] / [p0^x * (1−p0)^(n−x)]Let X be a binomial random variable. We can write the likelihood function as L(p) = [nCx px(1−p)n−x] . (b) Most powerful test: To derive the most powerful test, we need to find the likelihood ratio as LR = (p1/p0)x(1−p1/1−p0)n−x. Accept H0 if LR < c and reject H0 if LR ≥ c for some constant c.LRc= (0.8/0.5)^15*(0.2/0.5)^5 / (0.8/0.5)^15*(0.2/0.5)^5= (8/5)^15 = 34.99We reject H0 if the LR ≥ 34.99. Accept H0 if the LR < 34.99. (c) Reject H0 if the LR ≥ 34.99.LR = (0.8/0.5)15*(0.2/0.5)5 = 20.96Since 20.96 < 34.99, we accept H0. Therefore, at α = 0.1, we do not reject H0.

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The area of triangle will be 1/2*area of rectangle.

what exactly is a triangle?

A triangle is a geometric shape that consists of three line segments or sides, and three angles. Triangles are among the simplest and most fundamental shapes in geometry, and they are used in many fields of mathematics, science, engineering, and art.

The sum of the three interior angles of a triangle is always 180 degrees. The length of each side of the triangle is related to the size of the angles opposite to it, and to the length of the other sides, through various trigonometric functions.

Now,

The area of given triangle can be found by making a whole rectangle by making equal and parallel lines base and perpendicular.

let 1 box represent 1 unit if length

then area of rectangle=L*B

=5*4

=20 unit²

then, area of triangle=1/2*area of rectangle

=20/2

=10 unit²

hence,

           The area of triangle will be 1/2*area of rectangle.

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The improper fraction that is equivalent to 3 7/8 is 31/8.

A mixed number consists of a whole number and a proper fraction. In the case of 3 7/8, the whole number is 3 and the proper fraction is 7/8.

To convert a mixed number to an improper fraction, you need to first convert the whole number to a fraction by multiplying it by the denominator of the fraction in the mixed number. In this case, the denominator of the fraction is 8, so we multiply 3 by 8 to get 24.

Next, you add the numerator of the fraction to the result of the multiplication. In this case, the numerator is 7, so we add it to 24 to get 31.

3 7/8 = (3 x 8 + 7) / 8

= (24 + 7) / 8

= 31/8

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The given question is incomplete, the complete question is:

What is 3 7/8 as an improper fraction?

Deondra can purchase 2 amount outfits for $59.50 each within her budget of $420.

$420 - ($236.31 + $3.07 + $3.07 + $34.75) ≥ $59.50oo

$147.00 ≥ $59.50oo

$147.00 ÷ $59.50 ≥ oo

2.46 ≥ oo

Deondra can purchase 2 outfits.

Deondra has $420 to spend at a bicycle store for some new gear and biking outfits. She first buys a new bicycle for $236.31, then she buys two bicycle reflectors for $3.07 each and a pair of bike gloves for $34.75. In order to determine how many outfits she can purchase while staying within her budget, an inequality can be written and solved. The inequality is $420 - ($236.31 + $3.07 + $3.07 + $34.75) ≥ $59.50oo. This can be simplified to $147.00 ≥ $59.50oo. Dividing both sides of the inequality by $59.50, we get $147.00 ÷ $59.50 ≥ oo. After solving, this simplifies to 2.46 ≥ oo. Since Deondra can only purchase a whole outfit, the answer becomes 2 outfits. Therefore, Deondra can purchase 2 outfits while staying within her budget.

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The sheet would be approximately 93.13 cm wide if flattened out.

The length of an arc is determined by the degree measure of the central angle that subtends the arc. For example, if a circle has a radius of 5 units and an arc has a central angle of 90 degrees, the length of the arc can be found using the formula:

arc length = (central angle / 360) x 2πr

where r is the radius of the circle. In this case, the length of the arc would be:

arc length = (90/360) x 2π(5) = 1.25π units

The length of each arc can be found using the formula:

length = (angle / 360) x 2πr

where angle is the central angle of the arc in degrees, r is the radius of the arc, and π is pi (approximately equal to 3.14).

In this case, the radius is 10 cm and the central angle is 120 degrees, so the length of each arc is:

length = (120/360) x 2π(10) = (1/3) x 20π = (20/3)π cm

There are 14 such arcs in one sheet, so the total length of the sheet when flattened out is:

total length = 14 x (20/3)π = (280/3)π cm

This is approximately equal to 93.13 cm if we use the approximation π ≈ 3.14.

Therefore, the sheet would be approximately 93.13 cm wide if flattened out.

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The result of 3 divided by the difference of 4 and 2 is 1.5.

Formula:

3 / (4 - x)

Let's take the number x to be equal to 2.

Therefore, the calculation is 3 divided by the difference of 4 and 2, which is 3 / (4 - 2) or 3 / 2.

The answer is 1.5.

To explain further, when we divide the number 3 by the difference of 4 and 2, we are essentially dividing the number 3 by the result of subtracting 2 from 4. The result of subtracting 2 from 4 is 2. When we divide 3 by 2, the answer is 1.5.

Therefore, 3 divided by the difference of 4 and a number is equal to 1.5 when the number is equal to 2.

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Complete question:

What is 3 divided by the difference of 4 and a number?

After just a reflection along the [tex]X-axis[/tex], a quadrilateral [tex]MNOP[/tex] of position [tex]P[/tex] is [tex](3, -4)[/tex].

Four closed sides are making up a quadrilateral. Quadrilaterals are the following figures: Designed by Raphael. a four-sided figure. There is just one pair of parallel sides to the form, and there are no right angles.

A closed form known as a quadrilateral is known to be have sides with various widths and lengths. It is a closed polygon in two dimensions with four vertices, four angles, and four sides. Some examples of a quadrilateral are a cohesion and coherence, parallelogram, rectangle, rhombus, square, and kite.

When a point is reflected across the [tex]X-axis[/tex], the [tex]X-[/tex]coordinate stays the same, but the [tex]Y-[/tex]coordinate is multiplied by [tex]-1[/tex].

So to find the image of point [tex]P[/tex] after a reflection across the [tex]X-axis[/tex], we keep the [tex]X-[/tex]coordinate of [tex]P[/tex] the same (which is 3) and multiply the [tex]Y-[/tex]coordinate by [tex]-1[/tex]

New [tex]Y-[/tex]coordinate of [tex]P = -1 * 4 = -4[/tex]

Therefore, the image of point [tex]P[/tex] after a reflection across the [tex]X-axis[/tex] is [tex](3, -4)[/tex].

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Answer:

16.8π cm or 52.78 cm

Step-by-step explanation:

We are given the radius of one planet and the diameter of the other.

So, we have perimeter (circumference) of a circle is:

C = 2πr

where C is the circumference and r is the radius of the circle.

For the first planet with a radius of 16.8 cm, we can calculate its circumference as:

C1 = 2π(16.8) = 33.6π cm

For the second planet with a diameter of 16.8 cm, we can calculate its radius as half of the diameter:

r2 = d/2 = 16.8/2 = 8.4 cm

And then, we can calculate its circumference as:

C2 = 2π(8.4) = 16.8π cm

The difference between the perimeters of the two planets is:

C1 - C2 = (33.6π - 16.8π) cm

C1 - C2 = 16.8π cm

Therefore, the difference between the perimeters of the two planets is approximately 52.78cm, rounded to two decimal places.

The expression 1/2(2a + 1)(a + 3) can be described as the product of two expressions as 1/2 and (2a + 1)(a + 3).

The entire expression is the product of two smaller expressions, namely 1/2 and (2a + 1)(a + 3).

The second expression, (2a + 1)(a + 3), is a product of two binomials. Each binomial contains two terms separated by a plus sign.

The first binomial, 2a + 1, has a coefficient of 2 in front of the variable a and a constant term of 1. The second binomial, a + 3, has a coefficient of 1 in front of the variable a and a constant term of 3.

To simplify the expression 1/2(2a + 1)(a + 3), we can distribute the 1/2 to both terms inside the parentheses, resulting in the expression (a+1/2)(a+3).

The expression can be further simplified by multiplying the two binomials together, resulting in the quadratic expression a² + 7/2a + 3/2.

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Complete Question:

Consider the expression 1/2(2a + 1)(a + 3)

Complete 2 descriptions of the parts of the expression.

The tangent function is defined as the ratio of the sine function to the cosine function. It is periodic with a period of pi and has vertical asymptotes at odd multiples of pi/2. An equation for a tangent function with a domain of all real numbers and n as an integer is given by the following equation:
y = tan(x + n(pi))


The tangent function is defined as the ratio of the sine function to the cosine function, and it is periodic with a period of pi. It has vertical asymptotes at odd multiples of pi/2.
The tangent function can be represented by the following equation:
y = tan(x)
Where x is the angle measured in radians.
If we want to shift the graph of the tangent function by a certain amount, n, in the horizontal direction, we can use the following equation:
y = tan(x + n(pi))
Where n is an integer.
For example, if n = 2, then the graph of the tangent function would be shifted 2pi units to the left, and the equation would be:
y = tan(x - 2pi)
If n = 3, then the graph of the tangent function would be shifted 3pi units to the left, and the equation would be:
y = tan(x - 3pi)
And so on for any integer value of n.

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With this query, no effort is necessary. measure the tbsp. of all items.

A great source of both phosphorus and calcium, which are essential for the growth and upkeep of strong, strong teeth and bones, is milk. They lower the chance of developing osteoporosis and suffering broken bones later in life. Milk encourages strong bones.

1. Measure [tex]8[/tex] tbsp. chocolate sauce and add [tex]2\frac{1}{2}[/tex] cups of milk.

No work is required for this question. It is a simple instruction to measure out 8 tbsp. of chocolate sauce and add it to [tex]2\frac{1}{2}[/tex] cups of milk.

2. Start with [tex]1\frac{3}{4}[/tex] cups of milk and add [tex]2\frac{1}{2}[/tex] tbsp. chocolate sauce.

No work is required for this question. It is a simple instruction to start with [tex]1\frac{3}{4}[/tex] cups of milk and add [tex]2\frac{1}{2}[/tex] tbsp. of chocolate sauce.

3. Add [tex]3\frac{1}{3}[/tex] tbsp. chocolate sauce to [tex]1\frac{1}{4}[/tex] cups milk.

No work is required for this question. It is a simple instruction to add  [tex]3\frac{1}{3}[/tex]tbsp. of chocolate sauce to [tex]1\frac{1}{4}[/tex] cups of milk.

4. For every 1 cup of milk add [tex]2\frac{1}{2}[/tex] tbsp. of chocolate sauce.

No work is required for this question. It is a simple instruction to add [tex]2\frac{1}{2}[/tex] tbsp. of chocolate sauce for every [tex]1[/tex] cup of milk.

5. Stir [tex]1[/tex] tbsp. chocolate sauce into [tex]\frac{2}{3}[/tex] cup milk.

No work is required for this question. It is a simple instruction to stir 1 tbsp. of chocolate sauce into [tex]\frac{2}{3}[/tex] cup of milk.

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In number 292,389 the digit 3 have a value that is 10 times as great as the value of the digit 3 in 143,728.

What is a number?

A number is a mathematical value used for counting or measuring or labelling objects. Numbers are used to performing arithmetic calculations.

The value of a digit depends on its place value in a number. For example, the digit 3 in the number 143,728 has a value of 3 x 1,000 = 3,000 because it is in the thousands place.

Let's call the number we are looking for "x". We want to find a number where the value of the digit 3 is 10 times as great as the value of the digit 3 in 143,728.

The value of the digit 3 in x is 10 times the value of the digit 3 in 143,728, so we can set up the equation:

3 x place value of 3 in x = 10 x 3,000

Simplifying this equation, we get:

3 x place value of 3 in x = 30,000

Dividing both sides by 3, we get:

place value of 3 in x = 10,000

So the digit 3 in x must be in the ten thousands place. Now we can eliminate choices A and B, because they do not have a digit 3 in the ten thousands place.

Checking the remaining choices, we find that only choice C has a digit 3 in the ten thousands place, with a value of 3 x 10,000 = 30,000. Therefore, the answer is:

C. 292,389

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Answer:

We have:

a = 0

b = 1

f(x) = x³

f'(x) = 3x²

Using the Mean Value Theorem, we have:

f(b) - f(a) = f'(c)(b - a)

Substituting the given values:

f(1) - f(0) = f'(c)(1 - 0)

Simplifying the left side of the equation:

1³ - 0³ = 1

Simplifying the right side of the equation:

f'(c) = 3c²

Therefore:

3c² = 1

Solving for c:

c² = 1/3

c = ±√(1/3)

Since c must be between 0 and 1, we have:

c = √(1/3)

Therefore, c = √(1/3).

I hope this helps!

Answer:

586 square inches

Step-by-step explanation:

[tex]2((11(7) + 12(7) + 12(11))[/tex]

[tex]2(77 + 84 + 132)[/tex]

[tex]2(293) = 586[/tex]

The equatiοn fοr the relatiοnship between the net prοfit and the number οf tickets sοld is y = 70x - 1500.

In mathematics, an equatiοn is a statement that shοws the equality between twο expressiοns. The equatiοns can cοntain variables, cοnstants, and mathematical οperatiοns such as additiοn, subtractiοn, etc. In wοrd prοblems, the variables represent the unknοwn quantity οr unknοwn number

Here we have

A charity οrganizatiοn had tο sell a few tickets tο their fundraiser tο cοver necessary prοductiοn cοsts.  

Cοst οf each ticket =$70

Number οf tickets sοld = 10

Tοtal cοst οf 10 tickets = $ 70 × 10 = $ 700

Lοss after selling 10 tickets = $800    

Hence, tοtal cοst οf prοductiοn = $ 700 + $ 800 = $ 1500

Let's assume that they sοld 'x' tickets and gοt 'y' prοfit

=> Tοtal revenue gained by selling tickets = $ 70x  

Prοfit y = Tοtal revenue - Prοduct cοst  

=> y = 70x - 1500

Therefοre,

The equatiοn fοr the relatiοnship between the net prοfit and the number οf tickets sοld is y = 70x - 1500.

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Complete Question:

A charity organization had to sell a few tickets to their fundraiser just to cover necessary production costs. After selling 10 tickets, they were still at a net loss of $800 (due to the production costs). They sold each ticket for $70. Let y represent the net profit in dollars) when they have sold tickets. Complete the equation for the relationship between the net profit and the number of tickets sold.  

The number of ways to perform the task is 462.

In mathematics, a combination is a way of selecting items from a larger set in which the order of selection does not matter.

For example, if you are selecting a team of 3 people from a group of 10 people, the order in which you select the team members does not matter.

Here we have

Number of magazines = 11

Number of awards = 6

Using the combination formula,

No of ways to select 6 magazines out of 11 = C(11, 6)

= 11! / (6! × (11-6)!) = 11! / (6! × 5!) = 462  

Therefore,

The number of ways to perform the task is 462.

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Answer:

0.073(73h)

Step-by-step explanation:

[tex]0.08(73h)+73h[/tex]

[tex]=\dfrac{73}{100}(73h)+73h[/tex]

[tex]=73\%(73h)+73h[/tex]

Since, it took 50h to repair the computer so, 0.073(73h) represents the amount of tax Deborah has to pay. Which is 73% of 73h.

Yes, the political party can conclude that the Hispanic proportion of the population has changed since 2010

Now, let's look at the given information. In 2010, the percentage of Hispanic or Latino people in Oregon was 11.7%. This means that out of every 100 people in Oregon, approximately 12 were Hispanic or Latino.

The political party conducted a survey of 853 adults in Oregon and found that 113 of them were Hispanic or Latino. To determine if the percentage of Hispanic or Latino people in Oregon has changed since 2010, we need to compare the survey results to the 2010 percentage.

To do this, we can calculate the percentage of Hispanic or Latino people in the survey by dividing the number of Hispanic or Latino people in the survey (113) by the total number of people surveyed (853), and then multiplying by 100. This gives us a percentage of approximately 13.2%.

Using this formula, we can estimate the margin of error for this survey to be approximately +/- 2.8%.

This means that the true percentage of Hispanic or Latino people in Oregon could be as low as 10.4% or as high as 15.6%, based on the survey results.

Since the margin of error includes the 2010 percentage of 11.7%, we cannot conclude that the Hispanic proportion of the population has definitively changed based on this survey alone.

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The forecast for week 7 is 309

Given time series data for the problem is; Week 1Week 2Week 3Week 4Week 5Week 6Week 7Observed value220254280276297309Naive forecast220254280276297309Where, the forecast for the next week is the most recent value. It means that the forecast for week 7 is 309.The formula to calculate mean absolute error (MAE) is;$$\text{MAE}=\frac{1}{n}\sum_{i=1}^{n}|y_i-\hat{y}_i|$$Where, $n$ is the total number of observations, $y_i$ is the $i$th observed value, and $\hat{y}_i$ is the $i$th forecasted value by the naive method.MAE = $(1/7) \times (38+26+4+17+12+4+0)$ = 13.57Mean squared error (MSE) is given by;$$\text{MSE}=\frac{1}{n}\sum_{i=1}^{n}(y_i-\hat{y}_i)^2$$MSE = $(1/7) \times (38^2+26^2+4^2+17^2+12^2+4^2+0^2)$ = 3004.29Mean absolute percentage error (MAPE) is given by;$$\text{MAPE}=\frac{1}{n}\sum_{i=1}^{n}\left(\frac{|y_i-\hat{y}_i|}{y_i}\right)\times 100$$MAPE = $(1/7) \times [(38/220) + (26/254) + (4/280) + (17/276) + (12/297) + (4/309) + (0/309)] \times 100$MAPE = 5.17%Thus, (a) mean absolute error (MAE) is 13.57, (b) mean squared error (MSE) is 3004.29, (c) mean absolute percentage error (MAPE) is 5.17% and (d) the forecast for week 7 is 309.

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The length of the corresponding side of the larger polygon is 5/4.

What is polygon?

A polygon is a two-dimensional shape that is formed by connecting a sequence of straight lines (called sides or edges) end-to-end to form a closed loop. The term "poly" means "many," and "gon" means "angle," so a polygon literally means "many angles."

Polygons can have any number of sides, from three (a triangle) to infinity. The most common polygons are the quadrilateral (four sides), pentagon (five sides), hexagon (six sides), heptagon (seven sides), octagon (eight sides), nonagon (nine sides), and decagon (ten sides).

Let's assume that the smaller polygon has n sides and the larger polygon has m sides. Since the polygons are similar, their corresponding sides are proportional. Therefore, we can set up the following proportion:

n/m = 4/x

where x is the length of the corresponding side of the larger polygon.

We also know that the perimeter of the smaller polygon is 20, so each of its sides has length 20/n. Similarly, the perimeter of the larger polygon is 28, so each of its sides has length 28/m.

Since the polygons are similar, their corresponding sides are proportional, so we can set up another proportion:

(20/n) / (28/m) = 4/x

Simplifying this expression, we get:

20m = 28nx

Dividing both sides by 4, we get:

5m = 7nx

Substituting n/m = 4/x, we get:

5m = 28x

Solving for x, we get:

x = (5m)/28

Now, we need to find the value of m. The perimeter of the smaller polygon is 20, so the sum of its sides is 20. Since each side has length 20/n, we can write:

20 = (20/n)*n

Simplifying, we get:

n = 4

The perimeter of the larger polygon is 28, so the sum of its sides is 28. Since each side has length 28/m, we can write:

28 = (28/m)*m

Simplifying, we get:

m = 7

Now, we can substitute the value of m into the expression for x that we derived earlier:

x = (5m)/28 = (5*7)/28 = 5/4

Therefore, the length of the corresponding side of the larger polygon is 5/4.

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Answer:

------------

Step-by-step explanation:

Thanks...........

Answer:

25(5x - 2y)

Step-by-step explanation:

25 is the common factor for the equation. so the answer will be 25( 5x - 2y )

Answer:

i) here a=8 d=3 nth term= 8+(n-1)3

ii)50th term= 8+49×3=155

Step-by-step explanation:

i hope you find it helpful

Step-by-step explanation:

hope you understood the answer

The number of 11-inch softballs ordered is 70 and the number of 12-inch softballs ordered  is 50.

a + b = 120 equation 1

2.50a + 3.50b = 350 equation 2

Where:

The substitution method would be used to determine the number of each size of softball ordered.

Make a the subject of the formula in equation 1:

a = 120 - b

Substitute for a in equation 2:

2.50(120 - b) + 3.50b = 350

300 - 2.5b + 3.50b = 350

Combine and add similar terms:

3.5b - 2.5b = 350 - 300

b = 50

Substitute for b in equation 1

a + 50 = 120

a = 120 - 50

a = 70

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Answer: 22.4 cm

Step-by-step explanation:

Perimeter of sector is: P = 2r + 2πr(θ/360) P = 2*10 + 2(3.14) (135/360) = 22.4 cm (rounded)

Using the definition of a straight angle, the measure of angle MON is calculated as: 130°.

A straight angle is an angle that measures exactly 180 degrees. It is a flat angle, which means it has no curvature and looks like a straight line.

Therefore, we have:

m∠LOM + m∠MON = 180 [straight angle is equal to 180 degrees]

Substitute:

4x + 30 + 8x + 90 = 180

Solve for x:

12x + 120 = 180

12x = 180 - 120

12x = 60

x = 60/12

x = 5

m∠MON = 8x + 90° = 8(5) + 90

m∠MON = 130°

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Complete Question:

Given

m∠LON is a straight angle.

m∠LOM = 4x + 30°

m∠MON = 8x + 90°

Find m∠MON

from S^OH

sinθ=opp/hyp

sin38°=x/4

x=4sin38°

x=4×(0.61566147533)

x=(2.4626459013)

to 1dp

x=2.5cm

z = (x - np) / σ
z = (43 - 100(0.50)) / 0.05
z = -1.4
P(z > -1.4) = 0.9192

a) The number of working women in the sample is 100. The majority of women prefer a better 'work-life balance' to a higher salary, according to a global research study. The majority in percentage is 50% or greater, which implies that 50% of 100 working women or more prefer a better work-life balance to an increased salary. If we assume that the null hypothesis is correct and the number of women who say having a flexible work schedule is important is exactly 50, the standard error for the sample can be calculated as follows:

σ = sqrt(p(1-p)/n)
σ = sqrt(0.50(1-0.50)/100)
σ = 0.05

P(x<50) can be calculated as follows:

z = (x - np) / σ
z = (50 - 100(0.50)) / 0.05
z = -20
P(z < -20) = 0

Therefore, the probability that fewer than 50% of the sample say that having a flexible work schedule is either very important or extremely important to their career success is 0.

b) The proportion of women who said having a flexible work schedule is very important or extremely important to their career success is more than 43%. That implies the number of women in the sample who say having a flexible work schedule is important is greater than 43.

P(x > 43) can be calculated as follows:

z = (x - np) / σ
z = (43 - 100(0.50)) / 0.05
z = -1.4
P(z > -1.4) = 0.9192

Therefore, the probability that more than 43% of the sample says having a flexible work schedule is very important or extremely important to their career success is 0.9192.

Learn more about work-life balance

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