You plan to charge $1 for each time a student plays, and the payout for a win is $5. According to your calculations, the probability of a win is .05. What is your expected value for this game? The expected value

Answers

Answer 1

Answer:

- $0.75

Step-by-step explanation:

For each game played the chance of winning is 0.05 and losing is 0.95.

If the student wins, they get $5 -$1 = $4, but they lose $1.

Expected value is:

4*0.05 - 1*0.95 = -0.75

It means you will make $0.75 per average game.

Answer 2

Answer:

21.8

Step-by-step explanation:

Step 1

This is a problem on finding the mean of continuous grouped data. We first find the midpoint of each interval. For example, the first interval or class is 0 - 10. The mid-point of this class will be (0 + 10)/2 = 5.

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Step 2

We now calculate the product of mid-point and frequency for each class. Here, the number of athletes in each class is the frequency of that class. For example, for the first class 0 – 10, its frequency is 3.

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Step 3

We can now use the formula to calculate mean. Note that t...

You Plan To Charge $1 For Each Time A Student Plays, And The Payout For A Win Is $5. According To Your
You Plan To Charge $1 For Each Time A Student Plays, And The Payout For A Win Is $5. According To Your
You Plan To Charge $1 For Each Time A Student Plays, And The Payout For A Win Is $5. According To Your

Related Questions

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 444 gram setting. It is believed that the machine is underfilling the bags. A 41 bag sample had a mean of 440 grams with a variance of 441. Assume the population is normally distributed. A level of significance of 0.05 will be used. Specify the type of hypothesis test.

Answers

Answer:

The null hypothesis is [tex]H_0: \mu = 444[/tex]

The alternative hypothesis is [tex]H_1: \mu < 444[/tex]

The p-value of the test is 0.1148 > 0.05, which means that the sample does not give enough evidence to conclude that the machine is underfilling the bags.

Step-by-step explanation:

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 444 gram setting.

At the null hypothesis, we test if the machine works correctly, that is, the mean is of 444. So

[tex]H_0: \mu = 444[/tex]

At the alternative hypothesis, we test if they are underfilling, that is, if the mean is of less than 444. So

[tex]H_1: \mu < 444[/tex]

The test statistic is:

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.

444 is tested at the null hypothesis:

This means that [tex]\mu = 444[/tex]

A 41 bag sample had a mean of 440 grams with a variance of 441.

This means that [tex]n = 41, X = 440, s = \sqrt{441} = 21[/tex]

Value of the test statistic:

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{440 - 444}{\frac{21}{\sqrt{41}}}[/tex]

[tex]t = -1.22[/tex]

P-value of the test:

Right-tailed test(test if the mean is less than a value), with 41 - 1 = 40 df and t = -1.22.

Using a t-distribution calculator, this p-value is of 0.1148

The p-value of the test is 0.1148 > 0.05, which means that the sample does not give enough evidence to conclude that the machine is underfilling the bags.

Write an equation of the line that passes through a pair of points: (-5, -2), (3, -1) y=-x+ C. y=-- x - 11 11 a. 8 8 b. 11 d. y=-x+ 8 y=-x - 8 11​

Answers

Answer:

y = 8x+11

Step-by-step explanation:

The coordination of the points are : (-5,-2) , (3, -1)

Then, the equation is :

[tex]\frac{y+5}{x+2} =\frac{-5-3}{-2+1} \\\\or,\frac{y+5}{x+2} = 8\\or, y+5=8(x+2)\\or, y = 8x+16-5\\y= 8x+11[/tex]

Ophelia is making homemade spaghetti sauce by combining 48 oz of tomato paste with 6 cups of water.how many ounces of tomatoes paste are needed for every cup of water show your work.

Answers

Answer:

8 ounces of tomato paste for each cup of water.

Step-by-step explanation:

Just divide 48 / 6 to get 8 oz of tomato paste per cup of water.

Hope this helps!

Answer:  8 ounces

Work Shown:

48 oz of tomato paste = 6 cups of water

48/6 oz of tomato paste = 6/6 cups of water

8 oz of tomato paste = 1 cup of water

In short, we divide both values by 6 so that the "6 cups" becomes "1 cup". We can say the unit rate is 8 oz of tomato paste per cup of water.

please help me with this on the image

Answers

Answer: For flour it is 360g

3 eggs

900ml of milk

Step-by-step explanation:

Answer:

First, find the amount of ingredient for one pancake:

240 ÷ 8 = 30g of plain flour per pancake2 ÷ 8 = 0.25 eggs per pancake600 ÷ 8 = 75 ml of milk per pancake

Multiply that amount by 12 to find the amount needed for 12 pancakes:

30 x 12 = 360g of plain flour0.25 x 12 = 3 eggs75 x 12 = 900 ml of milk

A, B, and C are points of tangency. CQ = 5, PQ = 10, and PR = 14. What is the perimeter
of the triangle PQR?

Answers

*see attachment for diagram

Answer:

Perimeter = 38

Step-by-step explanation:

Recall: when two tangents are drawn to meet at a point outside a circle, the segments of the two tangents are congruent.

Given,

CQ = 5

PQ = 10

PR = 14

Perimeter of ∆PQR = RC + CQ + QB + BP + PA + AR

CQ = QB = 5 (tangents drawn from an external point)

BP = PQ - QB

BP = 10 - 5 = 5

BP = PA = 5 (tangents drawn from an external point)

AR = PR - PA

AR = 14 - 5 = 9

AR = RC = 9 (tangents drawn from an external point)

✔️Perimeter of ∆PQR = RC + CQ + QB + BP + PA + AR

= 9 + 5 + 5 + 5 + 5 + 9

Perimeter = 38

An isosceles right triangle has a hypotenuse that measures 4√2 cm. What is the area of the triangle?

Answers

Answer:

It would be B. 16 centimeters^2

Step-by-step explanation:

Find the missing length on this triangle

Answers

Answer:

Step-by-step explanation:

This is a geometric means problem where 60, the side common to both the triangles, is the geometric mean. Set it up like this:

[tex]\frac{36}{60}=\frac{60}{x}[/tex] and cross multiply to get

36x = 3600 so

x = 100

g Let the joint probability density function of random variables X and Y. (a) Calculate the marginal probability densities of X and Y . (b) Calculate the expected values of X and Y . be given by

Answers

Answer: hello your question is incomplete attached below is the complete question

answer:

a) Fx(X) = 0 ≤ x ≤ 2,    Fy(Y) = y - y^3/4

b) E(X) = 32/20 ,  E(Y) = 64/60

Step-by-step explanation:

a) Marginal probability density

Fx(X) = [tex]\int\limits^x_0 {\frac{xy}{2} } \, dy[/tex]

∴ probability density of X  = 0 ≤ x ≤ 2

Fy(Y) = [tex]\int\limits^2_y {\frac{xy}{2} } \, dx[/tex]

∴ probability density of Y = y - y^3/4

b) Determine the expected values of X and Y

E(X) = 32/20

E(Y) = 64 /60

attached below is the detailed solution

a. A contest entrant has a 0.002 probability of winning $12,165. If this is the only prize and the fee is $35, then find the expected value of winning the contest.
b. The probability of winning a lottery is 0.125, what is the probability of winning at least once in twelve trials?

Answers

Part (a)

If you win $12165, then you really net 12165-35 = 12130 dollars when you consider the ticket fee. So this is the true amount of money you win, or take home at the end of the day. This is before taxes.

Multiply 0.002 with 12,130 to get 0.002*12130 = 24.26

We'll use this later so let A = 24.26

The chances that you don't win are 1 - 0.002 = 0.998 which multiplies with -35 to indicate you lost $35 in playing the game. So we get B = 0.998*(-35) = -34.93

Lastly, add the values of A and B to get the expected value:

A+B = 24.26 + (-34.93) = -10.67 is the expected value.

On average, you expect to lose about $10.67 for any time you play the game.

Answer:  -10.67 dollars

===========================================================

Part (b)

0.125 is the probability of winning so 1-0.125 = 0.875 is the probability of losing.

Let's say you get really unlucky and lose 12 times in a row. Assuming each trial (aka case when you play the game) is independent, this would mean the probability of such an event is (0.875)^12 = 0.2014172, which is approximate.

Subtract that from 1 to get the probability of winning at least once

1 - (0.875)^12 = 1 - 0.2014172 = 0.7985828

which is also approximate. If we rounded to three decimal places, then it would be 0.799; I'm picking three decimals since 0.125 is to three decimal places. Round however you need to if otherwise.

Answer:  0.799 (approximate)

An industrial psychologist consulting with a chain of music stores knows that the average number of complaints management receives each month throughout the industry is 4, but the variance is unknown. Nine of the chain's stores were randomly selected to record complaints for one month; they received 2, 4, 3, 5, 0, 2, 5, 1, and 5 complaints. Using the .05 significance level, is the number of complaints received by the chain different from the number of complaints received by music stores in general?
1. Use the five steps of hypothesis testing.
2. Sketch the distributions involved
3. Explain the logic of what you did to a person who is familiar with hypothesis testing, but knows nothing about t tests of any kind. Be sure to explain how this problem differs from a problem with a known population variance and a single sample.

Answers

Answer: See explanation

Step-by-step explanation:

1. Use the five steps of hypothesis testing.

Step 1: The aim of the research is to conduct the five steps of hypothesis testing.

Step 2:

Null hypothesis: H0 u= 4

Population mean: H1 u = 4

Alternate hypothesis: u ≠ 4

Population mean: u ≠ 4

Step 3 and step 4 are attached.

Step 5: Based on the calculation, the calculated value of t is less than the t critical value, therefore, the null hypothesis will be failed to be rejected.

2. Sketch the distributions involved

This has been attached.

3. Explain the logic of what you did to a person who is familiar with hypothesis testing, but knows nothing about t tests of any kind.

The distribution is "t".

The means is tested by using T-test.

Chi-square is used to test the single variance.

Which of the following rational functions is graphed below?

Answers

Answer:

D. F(x) = [tex]\frac{1}{(x+4)}^{2}[/tex]

Subtract.

8 over 9 minus 1 over 3

Answers

Answer:

5 over 9

Step-by-step explanation:

multiplayer both sides of the second fraction by 3, then you have 3 over 9. So the problem becomes 8-3=5

A game consists of tossing three coins. If all three coins land on heads, then the player wins $75. If all three coins land on tails, then the player wins $45. Otherwise, the player wins nothing. On average, how much should a player expect to win each game

Answers

Answer:

On average, a player should expect to win $15.

Step-by-step explanation:

The expected value in an event with outcomes:

x₁, x₂, ..., xₙ

Each with probability:

p₁, ..., pₙ

is given by:

Ev = x₁*p₁ + ... +xₙ*pₙ

In this case we have 3 outcomes:

player wins $75 = x₁

player wins $45 = x₂

player does not win = x₃

Let's find the probabilities of these events.

player wins $75)

Here we must have the 3 coins landing on heads, so there is only one possible outcome to win $75

While the total number of outcomes for tossing 3 coins, is the product between the number of outcomes for each individual event (where the individual events are tossing each individual coin, each one with 2 outcomes)

Then the number total of outcomes is:

C = 2*2*2 = 8

Then the probability of winning $75 is the quotient between the number of outcomes to win (only one) and the total number of outcomes (8)

p₁ = 1/8

Win $45:

This happens if the 3 coins land on tails, so is exactly equal to the case above, and the probability is the same:

p₂ = 1/8

Not wining:

Remember that:

p₁ + p₂ + ... + pₙ = 1

Then for this case, we must have:

p₁ + p₂ + p₃ = 1

1/8 + 1/8 + p₃ = 1

p₃ = 1 - 1/8 - 1/8

p₃ = 6/8

Then the expected value will be:

Ev = $75*1/8 + $45*1/8 + $0*6/8 = $15

On average, a player should expect to win $15.

What is 2/11 as a decimal rounded to 3 decimal places?

Answers

Answer: The answer is 0.182

Hope this help :)

Which of the following is equivalent to the expression below?
8^11•8^x
A. 8^x-11
B. 8^11x
C. 8^11+x
D. 8^11-x

Answers

Answer:

C

Step-by-step explanation:

[tex] \sf {a}^{c} \times {a}^{b} = {a}^{b + c} \\ \sf = {8}^{11} \times {8}^{x} \\ \sf = {8}^{11 + x} (c)[/tex]

In this graph, which transformation can produce quadrilateral A′B′C′D′ from quadrilateral ABCD?

Answers

Answer:

A reflection across the y axis and then a reflection across the x axis

Step-by-step explanation:

Answer:

An 180 degree counterclockwise rotation around the origin

Step-by-step explanation:

plato/edmuntum answer

compound interest on a sum of money for 2 years compounded annually is Rs 8034 simple interest on the same sum for the same period and at the same rate is Rs 7800 find the sum and the rate of interest​

Answers

Here, we want to find the interest rate and principal

The interest rate, r = 6% and the principal, P = Rs 65,000

Compound interest:

A = P(1 + r/n)^t

Simple interest :

I = P * r * t

Simple interest for 2 years = Rs 7800

Simple interest for 1 year = Rs 7800 / 2

= Rs 3900

Compound interest for 2 years = Rs 8034

Compound interest for the second year = Rs 8034 - Rs 3900

= Rs 4134

Interest on Rs 3900 = Rs 4134 - Rs 3900

= Rs 234

Therefore,

Interest rate, r = 234/3900 × 100

= 0.06 × 100

r = 6%

Recall,

Simple interest :

I = P * r * t

Then,

P = I / r * t

= 3900 / 6% * 1

= 3900 / 0.06

= 65,000

P = Rs 65,000

https://brainly.in/question/1489411

Use the information below to complete the problem: p(x) = (1)/(x + 1)
and q(x) = (1)/(x - 1)
Perform the operation and show that it results in another rational expression.

p(x) - q(x)

Answers

Given:

The functions are:

[tex]p(x)=\dfrac{1}{x+1}[/tex]

[tex]q(x)=\dfrac{1}{x-1}[/tex]

To find:

The rational expression for [tex]p(x)-q(x)[/tex].

Solution:

We have,

[tex]p(x)=\dfrac{1}{x+1}[/tex]

[tex]q(x)=\dfrac{1}{x-1}[/tex]

Now,

[tex]p(x)-q(x)=\dfrac{1}{x+1}-\dfrac{1}{x-1}[/tex]

[tex]p(x)-q(x)=\dfrac{(x-1)-(x+1)}{(x+1)(x-1)}[/tex]

[tex]p(x)-q(x)=\dfrac{x-1-x-1}{x^2-1^2}[/tex]             [tex][\because a^2-b^2=(a-b)(a+b)][/tex]

[tex]p(x)-q(x)=\dfrac{-2}{x^2-1}[/tex]

Therefore, the required rational expression for [tex]p(x)-q(x)[/tex] is [tex]\dfrac{-2}{x^2-1}[/tex].

An election ballot asks voters to select three city commissioners from a group of six candidates. If your aunt and father are running, what is the probability that either your aunt or your father will become a city commissioner

Answers

Answer:

0.8 = 80% probability that either your aunt or your father will become a city commissioner.

Step-by-step explanation:

The candidates are chosen from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

6 candidates, which means that [tex]N = 6[/tex]

2 are the aunt and father, which means that [tex]k = 2[/tex]

3 are chosen, which means that [tex]n = 3[/tex]

What is the probability that either your aunt or your father will become a city commissioner?

Probability of at least one of them being chosen, which is:

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

In which

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 0) = h(0,6,3,2) = \frac{C_{2,0}*C_{4,3}}{C_{6,3}} = 0.2[/tex]

Then

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.2 = 0.8[/tex]

0.8 = 80% probability that either your aunt or your father will become a city commissioner.

Help please:))

2. When shipping ice cream, melting is understandably a big concern. You will notice that ice cream is not generally packaged in a cube-shaped container. A standard container of ice cream contains 1 L, or 1000 cm3 of ice cream,

a. What would be the optimal dimensions (radius and height) to minimize surface area?

b. What would the surface area be?

C. Suggest at least two reasons why this is different from the ice cream packaging that you see in the stores.​

Answers

Answer:

a) Because this asks about the radius and height, I assume that we are talking about a cylinder shape.

Remember that for a cylinder of radius R and height H the volume is:

V = pi*R^2*H

And the surface will be:

S = 2*pi*R*H + pi*R^2

where pi = 3.14

Here we know that the volume is 1000cm^3, then:

1000cm^3 = pi*R^2*H

We can rewrite this as:

(1000cm^3)/pi = R^2*H

Now we can isolate H to get:

H = (1000cm^3)/(pi*R^2)

Replacing that in the surface equation, we get:

S = 2*pi*R*H + pi*R^2

S = 2*pi*R*(1000cm^3)/(pi*R^2) + pi*R^2

S = 2*(1000cm^3)/R + pi*R^2

So we want to minimize this.

Then we need to find the zeros of S'

S' = dS/dR = -(2000cm^3)/R^2 + 2*pi*R = 0

So we want to find R such that:

2*pi*R = (2000cm^3)/R^2

2*pi*R^3 = 2000cm^3

R^3 = (2000cm^3/2*3.14)

R = ∛(2000cm^3/2*3.14) = 6.83 cm

The radius that minimizes the surface is R = 6.83 cm

With the equation:

H = (1000cm^3)/(pi*R^2)

We can find the height:

H = (1000cm^3)/(3.14*(6.83 cm)^2) =  6.83 cm

(so the height is equal to the radius)

b) The surface equation is:

S = 2*pi*R*H + pi*R^2

replacing the values of H and R we get:

S = 2*3.14*(6.83 cm)*(6.83 cm) + 3.14*(6.83 cm)^2 = 439.43 cm^2

c) Because if we pack cylinders, there is a lot of space between the cylinders, so when you store it, there will be a lot of space that is not used and that can't be used for other things.

Similarly for transport problems, for that dead space, you would need more trucks to transport your ice cream packages.

According to The Wedding Report, Inc., the mean cost for a wedding in the United States is $28732 (as of November 2008). Suppose the cost for a wedding is normally distributed with a standard deviation of $1500, and that a wedding is selected at random. Use the appropriate Excel function to calculate each of the following. (Note - Part (e) can be done by hand.)
(a) Find the probability that the wedding costs less than $22000.
(b) Find the probability that the wedding costs more than $32000.
(c) Find the probability that the wedding costs between $25000 and $30000.
(d) Find Q1 (the 25th percentile) and Q3 (the 75th percentile).
(e) Find the IQR for the wedding costs.
(f) The top 10% of weddings cost more than how much?

Answers

Answer:

Following are the solution to the given points:

Step-by-step explanation:

[tex]X = \text{cost of wedding}\sim \text{Normal}\ (\mu = 28732, \sigma= 1500)\\\\[/tex]

For point a:

[tex]Probability\ = 0.00000359\\\\ \text{(Using Excel function:} =NORMDIST(22000,28732,1500,1)).[/tex]

For point b:

[tex]Probability \ = 0.014678\\\\\text{(Using Excel function:} =1-NORMDIST(32000,28732,1500,1))\\\\[/tex]

For point c:

[tex]Probability\ = 0.794614436 \\\\[/tex]

[tex]\text{(Using Excel function:} \\=NORMDIST (30000,28732,1500,1)-NORMDIST(25000,28732,1500,1))\\\\[/tex]

For point d:

[tex]Q_1 = 27720.26537 \\\\\text{(Using Excel function:} =NORMINV(0.25,28732,1500)) \\\\Q_3 = 29743.73463 \\\\\text{(Using Excel function:} =NORMINV(0.75,28732,1500)).[/tex]

For point e:

[tex]IQR = Q_3 - Q_1 = 29743.73463 - 27720.26537 = 2023.469251.[/tex]

For point f:

[tex]Top\ 10\% = 30654.32735 \\\\\text{(Using Excel function:} =NORMINV(0.9,28732,1500)).[/tex]

Determine the number positive real zeros of the polynomial below. (Type answer in as a whole number)f(x)=x^5+3x^2-4x+2

Answers

Answer:

The number of positive real zeros is 2 or 0

Step-by-step explanation:

Given

[tex]f(x)=x^5+3x^2-4x+2[/tex]

Required

Number of positive real zeros

Using Descartes rule of signs;

We write out the signs in front of each term;

Sign = + + - +

Count the number of times the sign alternate; i.e. from positive to negative and from negative to positive

From positive to negative, we have: 1 (i.e. + - )

From negative to positive, we have: 1 (i.e. - +)

Add up the count

[tex]count = 1+1[/tex]

[tex]count = 2[/tex]

Hence, the number of positive real zeros is 2 or 0

Select the correct answer from the drop-down menu.

Answers

Answer:

-60 60 30 -30 one of it is answer

Point A lies outside of plane P, how many lines can be drawn parallel to plane P that pass through point A?

A. 0
B. 1
C. 2
D. an infinite number

Answers

Answer:

B. an infinite number

Step-by-step explanation:

Since point A lies outside of P, the number of lines that can be drawn parallel to P and passing through point A is only infinite. It is infinite because it is just one given point lying outside the plane. If there is more than one point then it will be otherwise.

Answer:

yeah

Step-by-step explanation:

add:7ab,8ab,-10ab,-3ab


Answers

Answer:

2ab

Step-by-step explanation:

7ab+8ab+(-10ab)+(-3ab)=

=15ab-13ab= 2ab

Answer:

2ab

Step-by-step explanation:

7ab+8ab+-10ab+-3ab

Factor out ab

ab(7+8-10-3)

ab(2)

2ab

Rudy Banks has won $5000 to attend university. If he invests the money in an
account at 12% per annum, compounded monthly, how much can he draw monthly
for the next 3 years?

Answers

Answer:

$7153.84

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Compounded Interest Rate Formula: [tex]\displaystyle A = P(1 + \frac{r}{n})^{nt}[/tex]

P is principle amountr is raten is compound ratet is time

Step-by-step explanation:

Step 1: Define

Identify variables

P = 5000

r = 12% = 0.12

n = 12

t = 3

Step 2: Find Interest

Substitute in variables [Compounded Interest Rate Formula]:                     [tex]\displaystyle A = 5000(1 + \frac{0.12}{12})^{12(3)}[/tex][Exponents] Multiply:                                                                                        [tex]\displaystyle A = 5000(1 + \frac{0.12}{12})^{36}[/tex](Parenthesis) Add:                                                                                            [tex]\displaystyle A = 5000(1.01)^{36}[/tex]Evaluate exponents:                                                                                         [tex]\displaystyle A = 5000(1.43077)[/tex]Multiply:                                                                                                             [tex]\displaystyle A = 7153.84[/tex]

Find the lateral surface area and volume of the solid object.

Answers

Answer:

See answers below

Step-by-step explanation:

Lateral surface area of a cone is expressed as:

L = πr√h²+r²

Given that

r = 11.5/2 = 5.75cm

h=16.6cm

L = 3.14(5.75)√16.6²+5.75²

L = 18.055√275.56+33.0625

L = 18.055*17.56

L=317.0458cm²

Volume = 1/3πr²h

Volume = 1/3π(5.75)²(16.6)

Volume = 1,723.34975/3

Volume = 574.45cm³

Whats The Correct Answer?!

Answers

Answer: the correct answer is D 0.05

Step-by-step explanation:

Answer:

0.02 m/s

Step-by-step explanation:

42/50 meters in 26/30 minutes,

26/30 minutes = 52 seconds

so in 1 second, 42/50 ÷ 52

= 42/50 × 1/52

= 21/1300

= 0.02 (approximately)

Answered by GAUTHMATH

The closing price of Schnur Sporting Goods Inc. common stock is uniformly distributed between $16 and $30 per share.
What is the probability that the stock price will be:_______
a) More than $25? (Round your answer to 4 decimal places.)
b) Less than or equal to $18? (Round your answer to 4 decimal places.)

Answers

Answer:

a) 0.3571 = 35.71% probability that the stock price will be more than $25.

b) 0.1429 = 14.29% probability that the stock price will be less than or equal to $18.

Step-by-step explanation:

Uniform probability distribution:

An uniform distribution has two bounds, a and b.

The probability of finding a value of at lower than x is:

[tex]P(X < x) = \frac{x - a}{b - a}[/tex]

The probability of finding a value between c and d is:

[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]

The probability of finding a value above x is:

[tex]P(X > x) = \frac{b - x}{b - a}[/tex]

Uniformly distributed between $16 and $30 per share.

This means that [tex]a = 16, b = 30[/tex]

a) More than $25?

[tex]P(X > x) = \frac{30 - 25}{30 - 16} = 0.3571[/tex]

0.3571 = 35.71% probability that the stock price will be more than $25.

b) Less than or equal to $18?

[tex]P(X < 18) = \frac{18 - 16}{30 - 16} = 0.1429[/tex]

0.1429 = 14.29% probability that the stock price will be less than or equal to $18.

Write an expression (or equation) that represents the number of square feet
of wallpaper you will need if the height of the family room is x feet, with a
length and width that are each 3 times the height of the room. The family
room has 1 door, which is 3 feet wide and 7 feet tall.

Answers

Answer: Given

room height is x feet

room length is 3x feet

room width is 3x feet

a door 3 ft wide by 7 ft tall

Find

The net area of the wall, excluding the door

Solution

The area of the wall, including the door, is the room perimeter multiplied by the height of the room. The room perimeter is the sum of the lengths of the four walls.

... gross wall area = (3x +3x +3x +3x)·x = 12x²

The area of the door is the product of its height and width.

... door area = (7 t)×(3 ft) = 21 ft²

Then the net wall area, exclusive of the door is ...

... net wall area = gross wall area - door area

... net wall area = 12x² -21 . . . . square feet

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