Which statistical test is most appropriate to use to answer the following research question? Is there a difference in mean height among middle school students based on gender (male and female) after controlling for age?

The required measure of Street K between Street C and D is 337.5 ft.

What is the equality of proportionality?

The equivalence between two ratios in algebra. A and B are in the same ratio as C and D in the formula a/b = c/d. When one of a proportion's four quantities is unknown, a proportion is often built up to resolve the word problem.

Here, we have

Given: In a certain city, E Street, W Street, C Street, and D Street are parallel streets that intersect K Street and M Street. How long K Street is between C Street and D Street is to be determined.

Let the distance of street K between C and D be x,

Now,

Taking the equality of the proportionality expression of triangles,

600 / 400 = 600 + x / 400 + 250

6 / 4 = 600 + x / 625

3750/4 = 600 + x

937.5 = 600 + x

x = 337.5

Hence, the required measure of Street K between Street C and D is 337.5 ft.

To learn more about the equality of proportionality from the given link

https://brainly.com/question/12242745

#SPJ1

The area of the square  is 196.1019 square inches

What is the area?

A two-dimensional figure's area is the amount of space it takes up. In other terms, it is the amount that counts the number of unit squares that span a closed figure's surface.

area of the circle = 3.14r² , r =radius

=> 153.94 = 3.14r²

=> r² = 153.94/3.14 = 49.0254

=> r= ± √ 49.0254 =± 7.0018

=> r= +  7.0018, r= - 7.0018

Consider positive value

r= +  7.0018

Diameter, d= 2r = 2*7.0018  = 14.0036 inches

Side (a) of square = Diameter = 14.0036 inches

The area of the square

= a²

= 14.0036²  square inches

= 196.1019 square inches

The area of the square  is 196.1019 square inches

To learn more about the area from the given link

https://brainly.com/question/25292087

#SPJ1

Therefore , the solution of the given problem of equation comes out to be y = (3 - √21) / 2

A straightforward regression curve is created using the equation y= mx+b. The y-intercept is m, and the slope is B. The phrase "math equation combining numerous variables" is sometimes used to describe the prior line even though it represents distinct components. Only two variables are present in bivariate linear equations. There are no known solutions to application issues involving linear equations. Y=mx+b.

Here,

Starting with the given equation:

1 - 2y/3 - y + 2y = 1/y + 2

Simplifying the left side:

1 - y/3 = 1/y + 2

Multiplying both sides by 3y:

3y - y² = 3 + 6y

Bringing all terms to one side:

y² + 3y - 3 - 6y = 0

Simplifying:

y² - 3y - 3 = 0

Using the quadratic formula:

y = (3 ± √21) / 2

Therefore, the solutions for y are:

y = (3 + √21) / 2

or

y = (3 - √21) / 2

To know more about linear equation visit:

brainly.com/question/11897796

#SPJ1

Answer: CHINA

Step-by-step explanation:

IAS CHINADU

Answer:

Bhutan is the answer.

Therefore , the solution of the given problem of equation  comes out to be 454 adult tickets and 733 student tickets were sold.

The formula y=mx+b is used to produce a simple regression curve. The slope is B, and the y-intercept is m. Despite the fact that the previous line represents distinct components, the phrase "math equation blending several variables" is frequently used to describe it. In bivariate linear equations, there are just two variables. Application problems involving linear equations have no known solutions. Y=mx+b, usually known as mx+b, presents an easy-to-understand set of equations.

Here,

Let x be the number of adult tickets sold, and y be the number of student tickets sold.

The total number of tickets sold is 1,187: x + y = 1187.

The total amount of money collected is $3,003: 5x + 1y = 3003.

We can use the first equation to solve for x in terms of y: x = 1187 - y.

Substituting this expression for x into the second equation, we get:

5(1187 - y) + y = 3003

Simplifying and solving for y, we get:

5935 - 4y = 3003

-4y = -2932

y = 733

So 733 student tickets were sold. To find the number of adult tickets sold, we can use either of the original equations. Let's use x + y = 1187:

x + 733 = 1187

x = 454

So 454 adult tickets were sold.

Therefore, 454 adult tickets and 733 student tickets were sold.

To know more about linear equation visit:

https://brainly.com/question/11897796

#SPJ1

When a fraction is equivalent to a percentage greater than 100, it means that the numerator represents a value that is greater than the denominator.

A percentage is a way to express a number as a fraction of 100. For example, 50% is the same as 50/100, which simplifies to 1/2.

Suppose we have a fraction that is equivalent to a percentage greater than 100, such as 125%. This means that the fraction represents 125 parts out of 100, or 125/100.

To simplify this fraction, we can divide both the numerator and denominator by the greatest common factor(GCF), which is 25 in this case. This gives us:

125/100 = (125 ÷ 25)/(100 ÷ 25) = 5/4

As we can see, the numerator (5) is greater than the denominator (4). This is because the original percentage value (125%) is greater than 100%, which means the fraction must have a numerator that is greater than the denominator to reflect this increase.

In general, if a fraction is equivalent to a percentage greater than 100, its numerator will be greater than its denominator because the percentage value represents a quantity that is greater than the whole (100%).

Learn more about the percentage here:

https://brainly.com/question/22593808

#SPJ9

Time  is 4.053 hours (to the nearest thousandth of an hour).

What is average rate?

This refers to  the change in speed over a selected period of time. It depends on when you take the measurements. •

Solving for average rate:

Average Rate = 123.362 mi per hr

Distance = 500 (mile)

Time =?

Average Rate = Distance

                            Time  

123.362 mi per hr =   500 (mile)

                                     Time    

Making time subject of the formular we have:

Time = 500 (mile)

            123.362 mi per hr

Time = 4.053 hrs

Time  is 4.053 hours  (to the nearest thousandth of an hour).

Learn more about average rate on

https://brainly.com/question/12395856

#SPJ1

The system of equations that shows the situation is option 1.  L+J=29  L=2J-10

The question tells us that the summation of the age of Latifa and Jameel is 29

Let J = Jameel

L = Latifa

L + J = 29

The question says that Latifa's age is 2 time of Jameels age = 2J with 10 years subracted

L = 2J - 10

Read more on equations here:https://brainly.com/question/2972832

#SPJ1

[tex]\textit{Partial Variation} \\\\ y = k_ox+k_1\hspace{5em}\textit{"y" varies partly with a constant and directly with "x"} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{"D" varies partly with a constant and directly with "V"}}{D=k_oV+k_1}\qquad \textit{we know that} \begin{cases} V=40\\ D=150\\[-0.5em] \hrulefill\\ V=54\\ D=192 \end{cases}[/tex]

[tex]\boxed{\begin{array}{llll} 150=40k_o+k_1\\\\ 192=54k_o+k_1 \end{array}}\qquad \stackrel{ \textit{using elimination method} }{\begin{array}{llll} -150=-40k_o-k_1\\\\ ~~ 192= ~~ 54k_o+k_1\\\cline{1-1} ~~ 42~= ~~ 14k_o+0 \end{array} }\qquad \implies 42=14k_o \\\\\\ \cfrac{42}{14}=k_o\implies \boxed{3=k_o}\hspace{5em}\stackrel{\textit{substituting on the 1st equation}}{150=40(3)+k_1}[/tex]

[tex]\cfrac{150}{40(3)}=k_1\implies \boxed{\cfrac{5}{4}=k_1}\hspace{5em} {\Large \begin{array}{llll} D=3V+\cfrac{5}{4} \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \textit{when V=73, what is "D"?}\qquad D=3(73)+\cfrac{5}{4}\implies D=\cfrac{881}{4}\implies D=220\frac{1}{4}[/tex]

Using the table and definition of inverse functions we will get:

f ⁻¹ (6) = 10.

Remember how inverse functions work, we know that for two inverse functions f(x) and f ⁻¹ (x)?

if f(x) =y

Then:

f ⁻¹ (y) = x

So now we want to find  f ⁻¹ (6), then if:

f ⁻¹ (6) = k

f(k) = 6

Looking at the table we can see that f(10) = 6, then f ⁻¹ (6) = 10.

Learn more about inverse functions at:

https://brainly.com/question/14391067

#SPJ1

let the total population be x

Step-by-step explanation:

38.8%of x=12,900,000

x=12,900,000*100/38.8

x=12,900,000*100*10/388

If a circular garden with a radius of 3 ft. Is bordered by a circular sidewalk that is 2 ft. Wide, then The area of the sidewalk is 28.26 ft².

To calculate this, first calculate the area of the garden, which is 28.27 ft² (A=πr²). After that subtract this from the area of the sidewalk, which is 56.54 ft² (A=π(r+2)²). The area of the sidewalk is the difference between these two values, which is 28.26 ft².

To calculate the area of the garden, we use the formula A=πr², where r is the radius of the garden. In this case, the radius is 3 ft., so the area is 28.27 ft². To calculate the area of the sidewalk, we use the formula

where r is the radius of the garden and 2 is the width of the sidewalk. In this case, the radius is 3 ft. and the width is 2 ft., so the area is 56.54 ft². The area of the sidewalk is then the difference between these two values, which is 28.26 ft².

Learn more about the area of the circle:

https://brainly.com/question/14068861

#SPJ4

Answer:

y - 7 = 2(x - 4)

Step-by-step explanation:

The equation of the line that goes through the points (4, 7) and (5, 9) is y - 7 = 2(x - 4). To find the equation of the line, you can use the point-slope form of the equation, which is y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a given point on the line. In this case, the given points are (4, 7) and (5, 9), and the slope is m = 2. Therefore, the equation of the line is y - 7 = 2(x - 4).

The input value is 7 for which h(x) = 3x-14 is equal to 0.

Graphs are visual representations of data that show how any two variables relate to one another. Without requiring a lot of words, they are frequently used to communicate complex and large amounts of data. A specific amount of data must be gathered through surveys or experiments before a graph may be created.

The graph's vertices

y is the coordinate

3, (−7,3), (5,3)

Otherwise put,

h(−7)=h(5)=x

The correct answer is x=5.

Essential Elements of a Graph.

choosing a graph that can accurately depict the kind of data generated

The horizontal axis (X-axis indicates the independent variable) and the vertical axis are the axes and scales (Y-axis represents the dependent variable).

Equally significant is the graph's caption, which explains the premise on which the graph was created without offering any interpretation or analysis of the data.

Pie charts are used to display data in groupings. The percentage of values is used to divide the full pie chart into segments. When there are only a few groups—say, six or fewer—pie charts are utilized.b

In a bar graph, both horizontal and vertical columns are used to plot the data. Higher values are represented by bars with longer lengths. As an illustration, consider the rising crop yield each year. When there are significant variances across categories, bar graphs are typically employed.

Line graph - A line graph is similar to a scatter plot, with the exception that it uses a continuous variable along the X-axis, such as time, temperature, height, and weight. For instance, a person's weight gain over a period of weeks.

The points on the graph

y -coordinate is  3, (−7,3), (5,3)  

In other words,  

h(−7)=h(5)=x  

We are asked for an input value other than  −7

so the answer is  x=5

To know more about the coordinate visit:

brainly.com/question/30574507

#SPJ1

The complete question is:

The amount that will be charged in prepaid interest on a $250,000 loan with an APR of 5.25% closed on April 12th is $9,457.19.

The APR represents the annual percentage rate.

The annual percentage rate is the interest rate for the year, including other finance charges.

To compute the interest, the annual percentage rate is multiplied by the loan amount and the period divided by 365 days.

Loan amount = $250,000

Annual percentage rate (APR) = 5.25%

Loan closing date = April 12th

April 12th to December 31st = 263 days

Interest for the year = $9,457.19 ($250,000 x 5.25% x 263/365)

Thus, for the year, the interest is $9,457.19.

Learn more about the annual percentage rate at https://brainly.com/question/28752423.

#SPJ1

Answer:

Step-by-step explanation:

a. The average rate of change in the number of worldwide cell phones can be calculated as:

Average rate of change = (change in number of cell phones) / (change in time)

The change in number of cell phones is 15.96 billion - 14.02 billion = 1.94 billion, and the change in time is 2 years. Therefore,

Average rate of change = 1.94 billion / 2 years = 0.97 billion/year

So, the average rate of change in the number of worldwide cell phones is 0.97 billion per year.

b. We can use the point-slope form of a linear equation to model the number of worldwide cell phones. Let t be the time in years since 2020, and C(t) be the number of worldwide cell phones in billions. Then the equation can be written as:

C(t) - 14.02 = 0.97t

Simplifying, we get:

C(t) = 0.97t + 14.02

So, the linear equation that models the number of worldwide cell phones is C(t) = 0.97t + 14.02.

c. To predict the number of cell phones that will be in use worldwide in the year 2027, we need to find the value of C(2027 - 2020) = C(7) using the linear equation we derived in part (b).

C(7) = 0.97(7) + 14.02 = 20.83 billion

Therefore, if the rate stays the same, we can predict that there will be 20.83 billion cell phones in use worldwide in the year 2027.

Answer:

32 degrees

Step-by-step explanation:

We know that the two opposite angles are equivalent so we need to figure out what each one equals.

First we find what x equals so:

9x - 55 = 5x + 21

When we solve for x we get 19 so we can put this back into the expression to find out the first angle

5(19) + 21 = 116

Since we know both sides are 116 we can add them and get 232

We know now that since all sides all add to 360 we can do

360-232= 128

then split 128 in two for the left and right sides we get 64 degrees

Since the line VU bisects the left angle we know the angle WOV is half of 64 which is:

32 degrees

If Precision Engineering Factory consumes 12,500 units of a component in every three- month period.  the total cost of material is TZS 6,060 per year.

The annual demand for the material can be calculated as follows:

Annual demand = (12,500 units/3 months) x (4 quarters/year) = 50,000 units/year

Ordering cost = TZS 3 per order

Number of orders = (50,000 units/year) / (12,500 units/order) = 4 orders/year

Ordering cost per year = (4 orders/year) x (TZS 3/order) = TZS 12/year

Trucking cost = TZS 12 per order

Trucking cost per year = (4 orders/year) x (TZS 12/order) = TZS 48/year

Deterioration and obsolescence cost = TZS 0.04 per unit per year

Deterioration and obsolescence cost per year = (50,000 units/year) x (TZS 0.04/unit/year) = TZS 2,000/year

Interest cost = TZS 0.06 per unit per year

Interest cost per year = (50,000 units/year) x (TZS 0.06/unit/year) = TZS 3,000/year

Storage cost = TZS 1,000 per year for 50,000 units

Storage cost per unit per year = (TZS 1,000/year) / (50,000 units) = TZS 0.02/unit/year

Storage cost per year = (50,000 units/year) x (TZS 0.02/unit/year) = TZS 1,000/year

Total cost of material = Ordering cost + Trucking cost + Deterioration and obsolescence cost + Interest cost + Storage cost

Total cost of material = TZS 12/year + TZS 48/year + TZS 2,000/year + TZS 3,000/year + TZS 1,000/year

Total cost of material = TZS 6,060/year

Therefore, the total cost of material is TZS 6,060 per year.

Learn more about total cost here:https://brainly.com/question/24214260

#SPJ1

The correct statements of the given ones are -

Two circles are said to be similar if the ratio of their corresponding radius, circumferance and areas are proportionally constant.

Given are the two circles such that circle P is similar to circle Q.

{ 1 } -

Circle Q is a dilation of circle P with a scale factor of 7.

Proof :

r{Q}/r{P} = 28/4 = 7

{ 2 } -

Circle Q is a translation of circle P, 6 units up.

Proof :

Apply the rule (x, y + 6) to the coordinate (2, -3), we get (2, 3).

Therefore, the correct statements of the given ones are -

To solve more questions on dilations, visit the link below -

brainly.com/question/30215119

#SPJ1

To make a batch of concrete with a total weight of 2200 pounds and a mix ratio of 5:4:2 for sand, gravel, and cement, we need 1000 pounds of sand, 800 pounds of gravel, and 400 pounds of cement.

We must utilise the ratio of sand, gravel, and cement in the mix, which is 5:4:2, to calculate the amount of each ingredient required for a batch of concrete with a total weight of 2200 pounds.

Let's use the number "5x" to represent the quantity of sand in the batch, where x is a proportionality constant. The batch's cement and gravel contents are then, respectively, "4x" and "2x," respectively.

The problem states that the batch weighs 2200 pounds in total. As a result, we may construct the equation shown below:

5x + 4x + 2x = 2200

By merging similar phrases to simplify the left side, we obtain:

11x = 2200

When we multiply both sides by 11, we get:

x = 200

Knowing the value of x allows us to calculate the quantity of each ingredient in the batch:

Sand weight is 5x, or 5 * 200, or 1000 pounds.

The gravel weight is 4x, or 4 * 200, or 800 pounds.

There are 400 pounds of cement, or 2x = 2 * 200.

Therefore we need 1000 pounds of sand, 800 pounds of gravel, and 400 pounds of cement to build a batch of concrete that weighs 2200 pounds overall and has a sand, gravel, and cement mix ratio of 5:4:2.

To know more similar question visit:

https://brainly.com/question/9282555

#SPJ1

The slope of the line tangent to the quadratic equation f(x) = x² + x + 8 is approximately equal to 27.996.

In this case we need to estimate the slope of a line tangent to a quadratic equation based on behavior exhibited by a set of secant lines. A secant line is a line that passes through only two points of the curve and a tangent line is a line that passes through only one point of the curve. The slope of the secant line can be determined by the following expression:

m = Δf(x) / Δx

Now we proceed to determine the slopes associated with each secant line:

x = 4

f(4) = 4² + 4 + 8

f(4) = 28

x = 4.1

f(4.1) = 4.1² + 4.1 + 8

f(4.1) = 28.91

x = 4.01

f(4.01) = 4.01² + 4.01 + 8

f(4.01) = 28.091

x = 3.9

f(3.9) = 3.9² + 3.9 + 8

f(3.9) = 27.110

x = 3.99

f(3.99) = 3.99² + 3.99 + 8

f(3.99) = 27.910

And the slope of the tangent line can be estimated by average:

m = 0.5 · [f(3.99) + f(4.01)]

m = 0.5 · (27.910 + 28.091)

m = 27.996

To learn more on tangent lines: https://brainly.com/question/28994498

#SPJ1

Answer:

(3/5) (30x - 15) = 72 ⇔ 18x - 9 = 72

(3/5) (30x - 15) = 72 ⇔ 3(6x - 3) = 72

(3/5) (30x - 15) = 72 ⇒ x = 4.5

Equation 1 and 2 have the same value.

Equations C and D have the same value.

A formula is given to us: 3/5 (30x -15) = 72. The equations with the same value of x are the ones we are to choose.

Let's tackle the issue at hand.

3/5 . 30x - 3/5 . 15=72

3.6x - 3.3= 72

18x - 9 = 72

As a result, option C is the best one.

As we factor 3 out of the equation above, we get:

3 . 6x - 3 . 3 = 72

3(6x-3)=72

As a result, option D is also a good decision.

Let's figure out what x is: 3(6x-3) / 3 = 72/3

6x-3=24

x = 4.5

As a result, the final choice is also right.

(3/5) (30x - 15) = 72⇔ 18x - 9 = 72

(3/5) (30x - 15) = 72 ⇔ 3(6x - 3) = 72

(3/5) (30x - 15) = 72 ⇒ x = 4.5

Equations C and D have the same value.

To learn more about equations from given link

https://brainly.com/question/16218335

#SPJ1

The requried, to avoid having her hours cut back, Bridgett must therefore manufacture more than 99 items.

A Z-score is stated as the fractional model of data point to the mean using standard deviations.

here, z = x - μ / σ

where, μ = mean and σ = standard daviation

Here,
We know that the distribution of items manufactured at Bridgett's job is normal with a mean (µ) of 100 and a standard deviation (σ) of 4. We also know that Bridgett needs to avoid performing in the lowest 40% of the distribution.

To find the minimum number of items that Bridgett needs to manufacture, we need to find the cutoff point below which the lowest 40% of the distribution falls. This cutoff point is the z-score that corresponds to the 40th percentile of the distribution.

Using a standard normal distribution table or calculator, we can find that the z-score that corresponds to the 40th percentile is approximately -0.25. This means that the lowest 40% of workers at Bridgett's job manufacture less than 100 - 0.25(4) = 99 items.

To avoid having her hours cut back, Bridgett must therefore manufacture more than 99 items.

Learn more about the z-score here:

brainly.com/question/13793746

#SPJ9

The solution of the given compound inequality in the interval notation is (∅).

What is compound inequality?

Inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using inequality symbols. Typically, we use the not equal symbol to indicate that two values are not equal.  But to compare the values, whether it is less than or greater than, different inequalities are used.

Given a compound inequality,

 1/4 x - 3  ≥ 1 and -3(x - 2) ≥ 2

To solve this we take the first inequality.

1/4 x - 3  ≥ 1

1/4 x ≥ 4

x ≥ 16

Now solve the second inequality.

-3(x - 2) ≥ 2

-3x +6 ≥ 2

-3x ≥ -4

x ≤ 4/3 (The inequality sign reverses because we are dividing by a negative number, -3)

Now from both solved inequalities, we can see that x should be greater than 16 as well as it should be less than 4/3.

There exists no such number.

Therefore the solution of the given compound inequality in the interval notation is (∅).

To learn more about inequalities, follow the link.

https://brainly.com/question/25275758

#SPJ1

So, in response to the above question, we can state that The projected sum is $800, or around $780. Hence, equation  of Mr. Foreman's estimation is accurate.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical. For examples, in the equation 3x + 5 = 14, because equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The emblem and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

Nine touchdowns by the Tigers, each earning six points, for a total of nine times six or 54 points.

The Leopards scored 5 touchdowns for a total of 5 x 6 = 30 points, each of which was worth 6.

We may deduct the total points scored by the Leopards from the total points scored by the Tigers to see how many more points the Tigers scored than the Leopards:

Leopards' points minus Tigers' points equals 54 - 30 = 24.

As a result, the formula is p, where p = 24, where Tigers' points Equal Leopards' points.

Hence, the Tigers outscored the Leopards by 24 points.

$105 + $448 + $115 + $143 - $21 = $790

We have the following by rounding the numbers to the closest tens:

$110 + $450 + $120 + $140 - $20 = $800

The projected sum is $800, or around $780. Hence, Mr. Foreman's estimation is accurate.

To know more about equation visit:

https://brainly.com/question/649785

#SPJ1

Answer:

1.15%

Step-by-step explanation:

The correct symbol for the given equation in the blank is the sign of non-equal to that ≠.

Equations are mathematical expressions that have two algebra on either side of an equal (=) sign. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a fundamental simple equation.

here, we have,

Let's solve the given equation,

3 (3+4) = 3³

3 (7) = 27

21 ≠ 27.

Therefore, it shows that LHS ≠ RHS.

To know more about equation:

brainly.com/question/10413253

#SPJ1

The solution to the system of equations: x + 3y = 7 and 2x + 4y = 8 is (-2, 3)

Isolate x in the first equation:

x + 3y = 7

x = 7 - 3y

Use the substitution method, Substitute the value for x into the second equation:

2x + 4y = 8

2(7 - 3y) + 4y = 8

Solve for y:

14 - 6y + 4y = 8

-2y = -6

y = 3

Substitute y into either original equation:

x + 3y = 7

x + 3(3) = 7

x + 9 = 7

x = -2

Write the solution as an ordered pair:

The solution is (-2, 3).

Learn more about substitution method here

brainly.com/question/14619835

#SPJ4

a) Note that  the probability that the 10th transistor  produced is the first with a defect is: ≈ 0.0171

b) The probability that the machine produces no defective transistors in a batch of 100 is: ≈ 0.1338

c) The expected value of a geometric distribution is 1/p, so the expected number of transistors before the first defective one is:  = 50

d) The expected value and standard deviation for the number of transistors produced before the first with a defect is ≈ 18.71

e)  Increasing the probability of an event affects the mean and standard deviation of the wait time until success in opposite ways.

(a) Since each transistor is independent, the probability that the 10th transistor produced is the first with a defect is the same as the probability that the first 9 transistors are not defective and the 10th one is defective. The probability that a transistor is not defective is 1 - 0.02 = 0.98. Therefore, the probability is:

P(1st defective on 10th) = (0.98)⁹ x 0.02 ≈ 0.0171

(b) The probability that the machine produces no defective transistors in a batch of 100 is:

P(no defects in 100) = (0.98)¹⁰⁰ ≈ 0.1338

(c) The number of transistors produced before the first with a defect follows a geometric distribution with parameter p = 0.02. The expected value of a geometric distribution is 1/p, so the expected number of transistors before the first defective one is:

E(X) = 1/p = 1/0.02 = 50

The variance of a geometric distribution is (1-p)/p², so the standard deviation is:

σ = √((1-p)/p²)

= √(0.98/0.0004)

≈ 22.36

(d) The expected value and standard deviation for the number of transistors produced before the first with a defect are calculated in the same way as in (c), but with a different value of p:

E(X) = 1/p = 1/0.05 = 20

σ = √((1-p)/p₂)

= √(0.95/0.0025)

≈ 18.71

(e) Increasing the probability of an event affects the mean and standard deviation of the wait time until success in opposite ways.

As the probability of an event increases, the expected wait time until success decreases. In other words, the mean becomes smaller. However, as the probability of an event increases, the variability in the wait time until success also increases.

Learn more about Probability:
https://brainly.com/question/11234923
#SPJ1

Answer:

(a) 0.0167

(b) 0.1326

(c) The expected value, mean, μ = 50        SD, σ = 49.4975

(d) The expected value, mean, μ = 20        SD, σ = 19.4936

(e) Increasing the probability of an event decreases the mean and standard deviation of the wait time until success.

Step-by-step explanation: