Let X be the damage incurred (in $) in a certain type of accident during a given year. Possible X values are 0, 1000, 5000, and 10000, with probabilities 0.81, 0.09, 0.08, and 0.02, respectively. A particular company offers a $500 deductible policy. If the company wishes its expected profit to be $100, what premium amount should it charge?

Answer:

[tex]\displaystyle -11 = x[/tex]

Step-by-step explanation:

3x + 15 = x - 7

- 3x + 7 - 3x + 7

____________

[tex]\displaystyle \frac{22}{-2} = \frac{-2x}{-2} \\ \\ -11 = x[/tex]

I am joyous to assist you anytime.

Answer: Can you please say your question clearer? I can't understand it.

Step-by-step explanation:

Answer:

can you please have a question to go with the problem

Step-by-step explanation:

Final answer:

The equation for the amount of money after x years is [tex]A = $4,000(1 + 0.068)^x[/tex]

Explanation:

The equation for the amount of money Kevin will have after x years considering a principal amount of $4,000 invested at a 6.8% annual interest rate with interest compounded annually is:

[tex]A = P(1 + r)^t[/tex]
Where:

Therefore, the compound interest formula for this investment is :

[tex]A = $4,000(1 + 0.068)^x[/tex]

Answer:

$64,000

Step-by-step explanation:

50,000+60,000+50000+70000+90000=320000

320000/5=64,000

Final answer:

To find the mean annual salary of the company's employees, add the individual salaries together to get a sum of $320,000, count the employees which are five in total, and then divide the total by the number of employees, resulting in a mean salary of $64,000.

Explanation:

To calculate the mean annual salary at the company, you first need to add together the salaries of all the employees. The total amount of the salaries is $50,000 + $60,000 + $50,000 + $70,000 + $90,000, which equals $320,000.

Next, you count the number of employees to determine how many values you have, which in this case is five, not six as the reference mistakenly suggests.

Finally, you divide the total sum of the salaries by the number of employees to find the mean salary. So, $320,000 divided by 5 equals $64,000. Therefore, the mean annual salary at the company is $64,000.

Answer:

The area function can be given as:

[tex]A(w)=w^2+0.6w[/tex]

Step-by-step explanation:

Given:

Width of the floor = [tex]w[/tex] meters

Length is 0.6 meters  longer than the width

To find the function rule that describes area [tex]A[/tex] of the floor of Micaela's room.

Solution:

Width of floor in meters = [tex]w[/tex]

So, length of the floor would be given in meters as = [tex](w+0.6)[/tex]

Area = [tex]length\times width[/tex]

Thus area [tex]A[/tex] of the floor as a function of width can be expressed as:

[tex]A(w)=w(w+0.6)[/tex]

Using distribution:

[tex]A(w)=w^2+0.6w[/tex]   (Answer)

Answer:

The number of bicycle that store sell each month to break even  is 13 bikes  .

Step-by-step explanation:

Given as :

The operation cost of bicycle store = $2400

The cost of payment by store at average rate = $60 per bike

The average selling price of each bike = s.p = $120 per bike

Let The number of bicycle that store sell each month to break even = n bikes

According to question

The operation cost of bicycle store = (cost of payment by store at average rate + average selling price of each bike ) × number of bicycle that store sell each month to break even

i.e ($60 per bike + $120 per bike) × n bikes = $2400

Or,  ($180 per bike) × n bikes = $2400

∴ 180 n = 2400

Or, n = [tex]\dfrac{2400}{180}[/tex]

i.e n = 13.333 ≈  13

So, The number of bicycle that store sell each month to break even = n = 13 bikes

Hence, The number of bicycle that store sell each month to break even  is 13 bikes  . Answer

Answer:

The Subtraction equation use to find the age of his oldest relative is [tex]x-79=5[/tex].

Step-by-step explanation:

Given:

Age of youngest  relative = 5 years

We need to write a subtraction equation that could be used to find the age of his oldest relative.

Solution:

Let the age of the oldest relative be 'x'.

Now given:

Age of youngest  relative is 79 years less than the age of his oldest relative.

So we can say that;

Age of oldest relative minus 79 is equal to Age of the youngest relative.

framing in equation form we get;

[tex]x-79=5[/tex]

Hence the Subtraction equation use to find the age of his oldest relative is [tex]x-79=5[/tex].

Final answer:

The subtraction equation to find the age of Curry's oldest relative, based on the given information, is x - 5 = 79. Solving this equation reveals that the oldest relative is 84 years old.

Explanation:

The question involves setting up a subtraction equation to find the age of Curry's oldest relative, given that the youngest relative is 5 years old and this is 79 years less than the age of the oldest relative. We can represent the age of the oldest relative as x. The equation is based on the information that the difference in age between the oldest and youngest relatives is 79 years. Therefore, the equation can be set up as x - 5 = 79.

To solve for x, which represents the age of the oldest relative, you would add 5 to both sides of the equation to isolate x on one side. This results in x = 84. So, the oldest relative is 84 years old.

The question stated has some missing statement part and question part in it.

Missing Statement Part:

t {weeks} ⇔ G(t) {games per week}

0⇔160

3⇔450

6⇔900

10⇔2100

12⇔2400

Missing Question Part:

Approximate the value of G'(8) using the data in the table. Show the computation that leads to the answer.

Answer:

300 games/week²

Step by Step Explanation:

[tex]G'(t)=\frac{dG(t)}{dt} \\[/tex]

i.e. change in values of function G(t) divided by change in change in time (weeks).

[tex]\frac{G(10)-G(6)}{10-6}\\ =\frac{2100-900}{4} \\=300[/tex]

The solution is (x, y) = (2, 3)

Solution:

Given equations are:

y = 3x - 3 ------- eqn 1

y = 2x - 1 ---------- eqn 2

We can solve the equations by substitution method

In eqn 1, we have y equals 3x - 3

If we substitute this in place of y in eqn 2, we can get value of "x"

Substitute eqn 1 in eqn 2

3x - 3 = 2x - 1

Move the variables to one side and constants to other side

3x - 2x = -1 + 3

Substitute x = 2 in eqn 1

y = 3(2) - 3

y = 6 - 3

Thus the solution is (x, y) = (2, 3)

Answer:

Rate of Interest is [tex]20\%[/tex]

Step-by-step explanation:

Given that

[tex]I=\$ 300, P=\$3000[/tex]

and T=0.5 years

To find rate of interest

We have I=PRT

Therefore

[tex]R=\frac{I}{PT}\times 100[/tex]

[tex]R=\frac{300}{(3000)(0.5)}\times 100[/tex]

[tex]=\frac{1}{10(0.5)}\times 100[/tex]

[tex]=20\%[/tex]

Therefore [tex]R=20\%[/tex]

Rate of Interest is [tex]20\%[/tex]

Answer:120

Step-by-step explanation:Total number of 3 pairs of socks=6

Socks pull in 2s n put back if not matching

P(n)=n!= 6!/3! =6×5×4×3×2/(3×2)

=120

Answer:

6.914miles (to 3 decimal places)

Step-by-step explanation:

Length of an arc = θ/360 *2πr

angle subtended by arc at the center of the earth = 6 minutes

1 minute =1/60 degree

6 minute= 6/60 degree =0.1°

θ=0.1°

radius of earth = 3960 miles

distance along the arc = [tex]\frac{0.1}{360}*2\pi *3960[/tex]

    =6.9142857143miles

The distance along an arc on the surface of the earth that subtends a central angle of 6 minutes is 6.912 miles

The length of an arc that subtends with a central angle of Θ in degree is given by:

arc length = (Θ/360) * 2πr

where r is the radius of the circle

Given that r = 3960 miles, θ = 6 minutes = (1/60 degree) * 6 = 1/10 degree

Therefore:

arc length = (1/10 ÷ 360) * 2π(3960) = 6.912 miles

Hence the distance along an arc on the surface of the earth that subtends a central angle of 6 minutes is 6.912 miles

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Answer:

knowledge base

Step-by-step explanation:

Knowledge base is a database used to retrieve information both in structured and unstructured form. It is like an online library.

These systems evaluate user input which can be keywords or phrases in English via artificial intelligence algorithms and return the desired output.

Knowledge management systems utilize a database management system (DBMS) to help users find information through natural language queries, facilitating the handling of large datasets and information retrieval across various fields.

Knowledge management systems use a large database called a database management system (DBMS) that allows users to find information by entering keywords or questions in normal English phrases. A DBMS is a software package that enables the creation, storage, maintenance, manipulation, and retrieval of large datasets distributed over one or more files.

For instance, systems like Microsoft Access, Oracle, FileMaker Pro, and Avanquest MyDataBase provide such functionalities that help in managing data efficiently.

These systems are crucial in handling vast amounts of information and assist in translating user queries into actionable data through a friendly interface designed to interpret natural language input. They are critical in various fields including personal, business, government, and scientific endeavors, facilitating a seamless flow of information.

Answer:

A. Esmeralda converted the mixed number to the wrong improper fraction.

D. Esmeralda did not divide –24 by 6 correctly.

E.  Esmeralda did not use the reciprocal of the divisor.

Step-by-step explanation:

Evaluating Esmerald's simplified expression, the errors in her evaluation are :

The appropriate evaluation procedure should be :

[tex]\frac{-5\frac{1}{4}}{\frac{3}{2}}[/tex]

Convert the Numerator to an improper fraction

[tex]\frac{\frac{21}{4}}{\frac{3}{2}}[/tex]

Take the reciprocal of the denominator

[tex]\frac{3}{2} = \frac{2}{3} [/tex]

Multiply the Numerator by the reciprocal of the denominator

[tex](-\frac{21}{4} )(\frac{2}{3}) = - \frac{42}{12} = -3 \frac{1}{2}[/tex]

Therefore, Esmeralda made three errors in her simplification procedure.

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Answer:

2.233444444e62 is the answer

Answer:

The Inequality representing money she can still spend on her friend birthday gift is [tex]15+x\leq 45[/tex].

Jordan can still spend at most $30 on her friends birthday gift.

Step-by-step explanation:

Given:

Total money need to spend at most = $45

Money spent on Yoga ball = $15

We need to find how much money she can still spend on her friend birthday gift.

Solution:

Let the money she can still spend on her friend birthday gift be 'x'.

So we can say that;

Money spent on Yoga ball plus money she can still spend on her friend birthday gift should be less than or equal to Total money need to spend.

framing in equation form we get;

[tex]15+x\leq 45[/tex]

The Inequality representing money she can still spend on her friend birthday gift is [tex]15+x\leq 45[/tex].

On solving the the above Inequality we get;

we will subtract both side by 15 using subtraction property of Inequality.

[tex]15+x-15\leq 45-15\\\\x\leq \$30[/tex]

Hence Jordan can still spend at most $30 on her friends birthday gift.

Answer: c. The mean is much larger than the median

Step-by-step explanation:

A dataset is skewed to the right when the peak of the dataset is located in the left( left of the mean), and it has a long right tail. It is also call positive skewed distribution. One of the characteristics of right skewed dataset is that the mean of the dataset is always greater/larger than the median and mode.

Therefore, for the case above if the mean is much larger than the median, it indicates that the dataset is skewed to the right.

A dataset is skewed to the right when the mean is much larger than the median. Therefore, the correct answer is option c.

When a dataset is skewed to the right, it means that the distribution of data is not symmetric, and it is stretched out more towards the higher values (right side) than the lower values (left side). This can be due to the presence of outliers or a natural characteristic of the data.

Now, let's look at why option "c" indicates right skewness:

c. The mean is much larger than the median.

The mean is the arithmetic average of all the values in the dataset, while the median is the middle value when the data is arranged in order. When a dataset is positively skewed (skewed to the right), it means that there are some significantly larger values in the right tail of the distribution that pull the mean to the right (towards higher values).

In this situation:

The mean gets pulled toward the larger values because the larger values have a greater impact on the mean due to their magnitude.

The median remains closer to the bulk of the data because it is not affected by extreme values as much as the mean.

So, when the mean is much larger than the median, it is an indication that there are significant outliers or a longer right tail in the dataset, which is a characteristic of a right-skewed distribution.

Therefore, the correct answer is option c.

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Answer: C. 225

Step-by-step explanation:

To get the total population (x), we will take the 40% of the total population and equate to 90

40%× x = 90

40/100 × x = 90

40x/100= 90

Cross multiplying,

40x = 100 × 90.

x = 9000/40

x =225 C

Answer:

the rise of the center of the rail will be given by =[tex]\sqrt{hypotenuse^{2}\hspace{0.15cm} -\hspace{0.15cm} base^{2} }[/tex]

= [tex]\sqrt{1500.065^{2} \hspace{0.15cm} -\hspace{0.15cm}1500^{2} }[/tex] m = 13.964 m

Step-by-step explanation:

i) the normal length of the railroad is 3 km = 3000 m.

ii) on a hot day day the railroad rail expands by 13cm  = 0.13m

iii) the center of the railroad is at 1500 m which is half of the total length.

iv) the expansion of the railroad in either half of the road is 0.065m which is half of the total expansion.

v) each half of the railroad can be represented by a right angled triangle whose base will be = 1500 m and hypotenuse will be = 1500.065 m .

vi) the rise of the center of the rail will be given by =[tex]\sqrt{hypotenuse^{2}\hspace{0.15cm} -\hspace{0.15cm} base^{2} }[/tex]

= [tex]\sqrt{1500.065^{2} \hspace{0.15cm} -\hspace{0.15cm}1500^{2} }[/tex] m = 13.964 m

The center of the rail would rise about 16.06 meters above the ground.

To find out how much the center of the rail rises above the ground due to expansion:

we can consider that the rail expands uniformly along its length.

If it expands by 13 cm over a length of 3 km, we can calculate the rise at the center using trigonometry, considering that the expansion causes the rail to form a very shallow arc.

The expansion forms a segment of a circle, where the rail length is the arc length, and the rise at the center is the height of the segment. We can use the formula for the height of a segment of a circle:

[tex]\[ h = r - \sqrt{r^2 - \left(\frac{l}{2}\right)^2} \][/tex]

Where:

h is the height of the segment (the rise at the center),

r  is the radius of the circle (which we can approximate as the radius of the Earth, as the rail is very long compared to its curvature),

l is the arc length of the segment (the expansion of the rail).

Given that the Earth's radius is approximately 6371 km, we need to convert all lengths to meters:

[tex]\[ r = 6371 \times 1000 \text{ meters} \][/tex]

[tex]\[ l = 3 \times 1000 \times 100 \text{ meters} \][/tex]

[tex]\[ h = 6371 \times 1000 - \sqrt{(6371 \times 1000)^2 - \left(\frac{3 \times 1000 \times 100}{2}\right)^2} \][/tex]

[tex]\[ h \approx 6371000 - \sqrt{(6371000)^2 - (150000)^2} \][/tex]

[tex]\[ h \approx 6371000 - \sqrt{40641464900000 - 22500000000} \][/tex]

[tex]\[ h \approx 6371000 - \sqrt{40641442400000} \][/tex]

[tex]\[ h \approx 6371000 - 6370983.94 \][/tex]

[tex]\[ h \approx 16.06 \text{ meters} \][/tex]

Answer:

Step-by-step explanation:

4x+y=14

x-2y=8

then;

x=8-2y

substitute;

4(8-2y)+8-2y=14

32-8y+8-2y=14

40-10y=14

26=10y

y=2.6 , work out 4x+2.6=14 to get x

Answer:

y=-2

x=4

Step-by-step explanation:

add 2y to both sides of equation 2

x-2y=8

x=8+2y

now that we have determined that x equals 2y, we can use it to substitute it in the first equation

4x+y=14

4(8+2y)+y=14

multiply 4 times the numbers in the parentheses

4(8+2y)+y=14

32+8y+y=14

isolate variables by subtracting 32 from both sides

32+8y+y=14

8y+y=-18

combine like terms

8y+y=-18

9y=-18

solve by dividing both sides by 9

9y=-18

y=-2

now that we know that y=-2, lets substitute it to solve for x

4x+y=14

4x-2=14

add 2 to both sides

4x-2=14

4x=16

divide both sides by 4

4x=16

x=4

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Answer:

1 3 5

Step-by-step explanation:

Answer:

Hallie ride 62 miles on bicycle.

Step-by-step explanation:

Given:

Let the number of miles Samantha rode be 'x'.

Hallie rode her bicycle 7 miles less than 3 times the number of miles Samantha rode.

It means that number of miles Hallie ride is equal to 3 multiplied by number of miles Samantha rode and then subtracting by 7.

framing in equation form we get;

number of miles Hallie ride = [tex]3x-7[/tex]

But Given:

number of miles Samantha rode =23 miles.

Now by substituting the value of [tex]x=23[/tex] in above equation we get;

number of miles Hallie ride = [tex]3x-7 = 3\times23-7 = 69-7 = 62 \ miles[/tex]

Hence Hallie ride 62 miles on bicycle.

Answer:

Condition 1:   y>0

Condition 2:  x+y>-2

Step-by-step explanation:

We are told that we have a set of points in the Cartesian system (i.e. x-y coordinate), so we can define our point as:

[tex](x,y)[/tex]

We are given two conditions and we want to create a system of inequalities. Now, generally speaking, inequalities are expressions relating mathematical expressions through 'comparison' (i.e. less than, greater than, or less/greater and equal to) usually recognized by [tex]<[/tex], [tex]>[/tex], [tex]\leq[/tex] and [tex]\geq[/tex], respectively.

So in our case let set up our inequalities.

Condition 1: the y-coordinate is positive

This can be mathematically translated as

[tex]y>0[/tex]

(i.e. [tex]y[/tex] is greater than 0, therefore positive)

Condition 2: the sum of the coordinates is more than -2

This can be mathematically translated as

[tex]x+y>-2[/tex]

(i.e. the summation of the two coordinates is greater than -2 but not equal to).

The system of inequalities described by the two conditions is:

[tex]y>0\\x+y>-2[/tex]

Final answer:

The two conditions given translate to the system of inequalities y > 0 and x + y > -2, which describe a specific region in the xy-coordinate plane.

Explanation:

The two conditions given by the student describe a certain region in the xy-coordinate plane. To translate these conditions into a system of inequalities, we first establish the inequality representation of each condition:

Condition 1 states that the y-coordinate is positive, which means any y value must be greater than zero. Therefore, this can be written as y > 0.

Condition 2 requires that the sum of the coordinates (x + y) is more than -2. Therefore, this inequality is x + y > -2.

Together, these two conditions form the following system of inequalities to describe the set of points in the xy-coordinate plane:

y > 0

x + y > -2

Final answer:

To find the dimensions of the larger boxes, you need to scale up each dimension by a factor of 2. The larger boxes will have dimensions of 8 inches in length, 6 inches in width, and 12 inches in height.

Explanation:

First, find the dimensions of the larger box. The larger box will have a length of 8 inches, which is twice the original length of 4 inches. Similarly, the width of the larger box will be 6 inches (twice the original width of 3 inches) and the height will be 12 inches (twice the original height of 6 inches).

Answer:

$309.18

Step-by-step explanation:

To pay off in 12 months = 12 * 657.80 = $7,893.6

To pay off in 18 months = 18 * 455.71 = $8202.78

If he takes the lower monthly payments, he will end up paying 8202.78 - 7893.6 = $309.18

The area of largest square is 225 m^2

Step-by-step explanation:

As the square are connected to the sides of right triangle

So,

The largest square will be the square connected to the hypotenuse as it is the longest side in the triangle

The area of square connected to the hypotenuse will be equal to the sum of areas of squares connected to the base and perpendicular of the right angled triangle.

Hence,

[tex]Hypotenuse^2 = Base^2+Perpendicular^2[/tex]

As we already know the area of square connected with the base

Putting the values

[tex]H^2 = 144 + (9)^2\\H^2 = 144+81\\H^2 = 225[/tex]

Hence,

The area of largest square is 225 m^2

Keywords: Pythagoras theorem, triangle

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Answer: It will take the largest pipe 5.5 hours to fill the swimming pool alone.

It will take the smallest pipe 16.5 hrs to fill the swimming pool alone.

It will take the other pipe 11 hours to fill the pool alone.

Step-by-step explanation: let time needed to fill the swimming pool by the largest pipe be x ... eq (1)

Let time needed to fill the swimming pool by the smallest pipe be 3x ... eq(2)

Let time needed to fill the swimming pool by the other pipe be 2x ...eq(3)

The job to be done (to fill a swimming pool) be 3/x +3/3x+3/2x=1 ... eq(4)

Multiply 6x on both sides you will get:

6(3)+2(3)+3(3)=6x

18+6+9=6x

33=6x

33/6=x

X=5.5hours

Substitute x=5.5 into EQ 2 and 3

3x=3×5.5=16.5hours

2x=2×5.5=11hours

Check: substitute the value of x into eq3/5.5+3/16.5+3/11

0.545+0.182+0.273=0.9997=1

Answer:

Step-by-step explanation:

a)

p(d) - probability of a rivet being defective

p(r) - probability of seam needing to be reworked

The probability of the seem needing to be reworked is equal to the probability that ANY of 24 rivets is defective

Thus the probability that none of the 25 rivets is defective is 1-p(r)

p(r) = 16%, thus 1-p(r) = 84%

1-p(r) = (1-p(d))^24

0.84 = (1-p(d))^24

0.84^(1/24) = 1-p(d)

==> 1-p(d) = 0.9927615998

==> p(d) = 1-0.9927

==> p(d) = 0.0073

b) given p(r) = 8%, thus 1-p(r) = 92%

1-p(r) = (1-p(d))^24

0.92 = (1-p(d))^24

0.92^(1/24) = 1-p(d)

==> 1-p(d) = 0.99653179446

==> p(d) = 1-0.9965

==> p(d) = 0.0035

Answer:

a) [tex]P(X<175) = P(Z<\frac{175-183}{10.5}) =P(Z<-0.762)[/tex]

[tex]P(z<-0.762)=0.223[/tex]

b) [tex]P(X>195) =P(Z>\frac{195-183}{10.5})=P(Z>1.143)[/tex]

[tex]P(z>1.143)=1-P(Z<1.143) =1-0.873=0.127[/tex]

c) [tex]P(173<X<193)=P(\frac{173-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{193-\mu}{\sigma})=P(\frac{173-183}{10.5}<Z<\frac{193-183}{10.5})=P(-0.953<z<0.953)[/tex]

[tex]P(-0.953<z<0.953)=P(z<0.953)-P(z<-0.953)[/tex]

[tex]P(-0.953<z<0.953)=P(z<0.953)-P(z<-0.953)=0.830-0.170=0.660[/tex]

d) [tex]P(\bar X >190)=P(Z>\frac{190-183}{\frac{10.5}{\sqrt{1000}}}=21.08)[/tex]

And using a calculator, excel ir the normal standard table we have that:

[tex]P(Z>21.08)=1-P(Z<21.08) \approx 0[/tex]

So for this case we expect anyone with a heigth higher than 190 cm in a random sample of 1000.

Step-by-step explanation:

Previous concepts

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

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Part a

Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(183,10.5)[/tex]  

Where [tex]\mu=183[/tex] and [tex]\sigma=10.5[/tex]

We are interested on this probability

[tex]P(X<175)[/tex]

And the best way to solve this problem is using the normal standard distribution and the z score given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

If we apply this formula to our probability we got this:

[tex]P(X<175) = P(Z<\frac{175-183}{10.5}) =P(Z<-0.762)[/tex]

And we can find this probability with the normal standard table or with excel:

[tex]P(z<-0.762)=0.223[/tex]

Part b

[tex]P(X>195)[/tex]

[tex]P(X>195) =P(Z>\frac{195-183}{10.5})=P(Z>1.143)[/tex]

And we can find this probability with the normal standard table or with excel: using the complement rule

[tex]P(z>1.143)=1-P(Z<1.143) =1-0.873=0.127[/tex]

Part c

[tex]P(173<X<193)[/tex]

And the best way to solve this problem is using the normal standard distribution and the z score given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

If we apply this formula to our probability we got this:

[tex]P(173<X<193)=P(\frac{173-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{193-\mu}{\sigma})=P(\frac{173-183}{10.5}<Z<\frac{193-183}{10.5})=P(-0.952<z<0.953)[/tex]And we can find this probability on this way:

[tex]P(-0.953<z<0.953)=P(z<0.953)-P(z<-0.953)[/tex]

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.  

[tex]P(-0.953<z<0.953)=P(z<0.953)-P(z<-0.953)=0.830-0.170=0.660[/tex]Part d

Since the distributiion for X is normal then the distribution for the sample mean is also normal and given by:

[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]

And we eant this probability:

[tex]P(\bar X >190)=P(Z>\frac{190-183}{\frac{10.5}{\sqrt{1000}}}=21.08)[/tex]

And using a calculator, excel ir the normal standard table we have that:

[tex]P(Z>21.08)=1-P(Z<21.08) \approx 0[/tex]

So for this case we expect anyone with a heigth higher than 190 cm in a random sample of 1000.

The probability that a Dutch male is shorter than 175 cm is approximately 0.2236. The probability that a Dutch male is taller than 195 cm is approximately 0.1271. The probability that a Dutch male is between 173 and 193 cm is approximately 0.6578.

a. To find the probability that a Dutch male is shorter than 175 cm, we need to calculate the z-score. The z-score formula is Z = (X - μ) / σ, where X is the value we're interested in, μ is the mean, and σ is the standard deviation. In this case, X = 175 cm, μ = 183 cm, and σ = 10.5 cm. Plugging these values into the formula, we get Z = (175 - 183) / 10.5 = -0.7619. Using a standard normal distribution table or calculator, we can find the corresponding probability, which is about 0.2236.

b. To find the probability that a Dutch male is taller than 195 cm, we can use the same process as in part a. The z-score for 195 cm is Z = (195 - 183) / 10.5 = 1.1429. Using the standard normal distribution table or calculator, we can find the probability of being less than 1.1429, which is about 0.8729. Since we want the probability of being taller, we subtract this value from 1 to get 1 - 0.8729 = 0.1271.

c. To find the probability that a Dutch male is between 173 and 193 cm, we need to calculate the z-scores for both heights. The z-score for 173 cm is Z = (173 - 183) / 10.5 = -0.9524, and the z-score for 193 cm is Z = (193 - 183) / 10.5 = 0.9524. Using the standard normal distribution table or calculator, we can find the probabilities for each z-score: P(Z < -0.9524) ≈ 0.1711 and P(Z < 0.9524) ≈ 0.8289. The probability of being between 173 and 193 cm is the difference between these two values, which is approximately 0.8289 - 0.1711 = 0.6578.

d. To find the number of Dutch men expected to be taller than 190 cm in a random sample of 1000, we can use the mean and standard deviation to calculate the z-score for 190 cm. The z-score is Z = (190 - 183) / 10.5 = 0.6667. Using a standard normal distribution table or calculator, we can find the probability of being less than 0.6667, which is about 0.7475. Multiplying this probability by the sample size, we get 0.7475 * 1000 = 747.5. Therefore, we would expect approximately 748 Dutch men in the sample to be taller than 190 cm.

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Answer:

Option (c) 9.46%

Step-by-step explanation:

Amount deposited by Eric = $100

Amount deposited by Mike = $200

Interest rate = i

Now,

For Eric

Amount after 7.5 years, A = Principle × [tex]( 1 +\frac{i}{2})^{2\times15}[/tex]

=  $100 × [tex]( 1 +\frac{i}{2})^{2\times15}[/tex]

thus,

for the last 6 months i.e 0.5 year =  A × [tex]( 1 +\frac{i}{2})^{2\times0.5}[/tex]

= A × [tex]( 1 +\frac{i}{2})^{1}[/tex]

therefore,

Interest earned = A × [tex]( 1 +\frac{i}{2})^{1}[/tex] - A

= A × [tex]( \frac{i}{2})[/tex]

= $100 × [tex]( 1 +\frac{i}{2})^{2\times15}\times( \frac{i}{2})[/tex]

= $50i [tex]\times( 1 +\frac{i}{2})^{2\times15}[/tex] ......(1)

For Mike

Interest  = Principle × i × Time

= $200 × i × 0.5

= $100i .........(2)

Equating (1) and (2)

$50i [tex]\times( 1 +\frac{i}{2})^{2\times15}[/tex] = $100i

or

[tex]( 1 +\frac{i}{2})^{2\times15}[/tex] = 2

or

[tex]( 1 +\frac{i}{2})[/tex]  = 1.0473

or

[tex]\frac{i}{2}[/tex]   =  1.0473 - 1

or

[tex]\frac{i}{2}[/tex]  = 0.0473

or

i = 0.0946

or

i = 0.0946 × 100% = 9.46%

Hence,

Option (c) 9.46%