Assume you have a ticket that will let you participate in a game of chance (a lottery) that will pay off $10 with a 45% chance (or a 55% chance of getting nothing). Your friend has a ticket to a different lottery that has a 20% chance of paying $25 (or an 80% chance of paying nothing). Your friend has offered to let you have his ticket if you will give him your ticket plus one dollar.

Required:
Build an influence diagram for this problem.

Answer:

The minimum sample size is 1,704.

Step-by-step explanation:

We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a p-value of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

Standard deviation of 21,059,637 shares

This means that [tex]\sigma = 21059637[/tex]

What is the minimum required sample size if you would like your sampling error to be limited to 1,000,000 shares?

This is n for which [tex]M = 1000000[/tex], so:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]1000000 = 1.96\frac{21059637}{\sqrt{n}}[/tex]

[tex]1000000\sqrt{n} = 1.96*21059637[/tex]

[tex]\sqrt{n} = \frac{1.96*21059637}{1000000}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96*21059637}{1000000})^2[/tex]

[tex]n = 1703.8[/tex]

Rounding up:

The minimum sample size is 1,704.

From the data given, we estimate the population mean and population standard deviation. Then, we use this estimate to find a 95% confidence interval for the population variance and the population standard deviation.

Sample:

Salaries in millions of dollars: 2.2, 1.5, 0.5, 1.3, 2.4, 1.5, 2.7, 0.3, 2.0, 0.3

Question a:

The mean is the sum of all values divided by the number of values. So

[tex]\overline{x} = \frac{2.2 + 1.5 + 0.5 + 1.3 + 2.4 + 1.5 + 2.7 + 0.3 + 2.0 + 0.3}{10} = 1.42[/tex]

The sample mean salary is of 1.42 million.

Question b:

The standard deviation is the square root of the difference squared between each value and the mean, divided by one less than the number of values.

So

[tex]s = \sqrt{\frac{(2.2-1.42)^2 + (1.5-1.42)^2 + (0.5-1.42)^2 + (1.3-1.42)^2 + (2.4-1.42)^2 + (1.5-1.42)^2 + (2.7-1.42)^2 + ...}{9}} = 0.8772[/tex]

Thus, the estimate for the population standard deviation is of 0.8772 million.

Question c:

The sample size is [tex]n = 10[/tex]

The significance level is [tex]\alpha = 1 - 0.05 = 0.95[/tex]

The estimate, which is the sample standard deviation, is of [tex]s = 0.8772[/tex].

Now, we have to find the critical values for the Pearson distribution. They are:

[tex]\chi^2_{\frac{\alpha}{2},n-1} = \chi^2_{0.025,9} = 19.0228[/tex]

[tex]\chi^2_{1-\frac{\alpha}{2},n-1} = \chi^2_{0.975,9} = 2.7004[/tex]

The confidence interval for the population variance is:

[tex]\frac{(n-1)s^2}{\chi^2_{\frac{\alpha}{2},n-1}} < \sigma^2 < \frac{(n-1)s^2}{\chi^2_{1-\frac{\alpha}{2},n-1}}[/tex]

[tex]\frac{9*0.8772^2}{19.0228} < \sigma^2 < \frac{9*0.8772^2}{2.7004}[/tex]

[tex]0.3641 < \sigma^2 < 2.5646[/tex]

Thus, the 95% confidence interval for the population variance is (0.3641, 2.5646)

Question d:

Standard deviation is the square root of variance, so:

[tex]\sqrt{0.3641} = 0.6034[/tex]

[tex]\sqrt{2.5646} = 1.6014[/tex]

The 95% confidence interval for the population standard deviation is (0.6034, 1.6014).

For more on confidence intervals for population mean/standard deviation, you can check https://brainly.com/question/13807706

Answer:

0.6524 = 65.24% probability that the runner will average between 146 and 150 minutes in these 49 marathons.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Average of 147 minutes with a standard deviation of 12 minutes.

This means that [tex]\mu = 147, \sigma = 12[/tex]

Consider 49 of the races.

This means that [tex]n = 49, s = \frac{12}{\sqrt{49}} = \frac{12}{7} = 1.7143[/tex]

Find the probability that the runner will average between 146 and 150 minutes in these 49 marathons.

This is the p-value of Z when X = 150 subtracted by the p-value of Z when X = 146. So

X = 150

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{150 - 147}{1.7143}[/tex]

[tex]Z = 1.75[/tex]

[tex]Z = 1.75[/tex] has a p-value of 0.9599

X = 146

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{146 - 147}{1.7143}[/tex]

[tex]Z = -0.583[/tex]

[tex]Z = -0.583[/tex] has a p-value of 0.3075.

0.9599 - 0.3075 = 0.6524.

0.6524 = 65.24% probability that the runner will average between 146 and 150 minutes in these 49 marathons.

Answer:

There are 666 numbers multiple of 3 in the interval.

Step-by-step explanation:

Multiples of 3:

A number is a multiple of 3 if the sum of it's digits is a multiple of 3.

Range [2,2000]:

First multiple of 3 in the interval: 3

Last: 1998

How many:

[tex]1 + \frac{1998 - 3}{3} = 1 + 665 = 666[/tex]

There are 666 numbers multiple of 3 in the interval.

Answer:

12

Step-by-step explanation:

If f(x) = 5 - x

Then f(-7) = 5 - (-7)

f(-7) = 5 + 7

f(-7) = 12

Answer:

X-(-7)

Step-by-step explanation:

If you are subtract by a negative number it turns it into a positive. It would look like this: X+(+7)

Answer:

I think the answer is B. 65%

Answer:

Each group has 1 fiction book and 2 nonfiction book(s).

Answer:

A.  5

Step-by-step explanation:

Parallel lines have the same slope.

Answer:

5

Step-by-step explanation:

Answer:

Step-by-step explanation:

Speed = (15 mi)/hr × (1.6 km)/mi = (24 km)/hr

:::::

(4 hr) × (24 km)/hr = 96 km

The required probability of a couple having a baby boy when their third child is​ born is 1/2.

probability is the ratio of the number of favorable outcomes and the total number of possible outcomes. The chance that a particular event (or set of events) will occur expressed on a linear scale from 0 (impossibility) to 1 (certainty), also expressed as a percentage between 0 and 100%.

Given:

Assuming boys and girls are equally​ likely.

The first two children were both boys

According to given question we have

The probability of having a baby girl is an independent probability.

The first two children were both boys

So, it is not related to the previous child.

So required probability = 1/2

Therefore, the required probability of a couple having a baby boy when their third child is​ born is 1/2.

Learn more details about probability here:

https://brainly.com/question/11234923

#SPJ2

Answer:

$3792116

Step-by-step explanation:

that's the answer above

Answer:

c

Step-by-step explanation:

The first four terms are 17, 15, 13, and 11.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(n):

f(1) = 17

f(n) = f(n - 1) - 2 if n > 1

Now,

The first term is 17.

The second term.
f(2) = f(2 - 1) - 2

= f(1) - 2

= 17 - 2

= 15

The third term.

= f(3 - 1) - 2

= f(2) - 2

= 15 - 2

= 13

The fourth term.

f(4) = f(4 - 1) - 2
= f(3) - 2

= 13 - 2

= 11

Thus,

The terms are 17, 15, 13, 11

Learn more about functions here:

https://brainly.com/question/28533782

#SPJ2

Answer:

diện tích đa giác trong hình là :

186 cm2

Step-by-step explanation:

hãy tách hình đa giác trên thành 4 hình chữ nhật và tính diện tích từng hình chữ nhật

Answer:

a. 168000 for Eyeconnect, 132000 for Topconnect

b. 100,000

Step-by-step explanation:

a.

Because the change in customers are only due to leaving companies, we can say that, after one year, Eyeconnect loses 10% of its customers to Topconnect and Topconnect loses 5% of its customers to Eyeconnect. This represents all changes in customers.

First, we can calculate how much Eyeconnect loses, which is 10% of 180,000 = 0.1 * 180,000 = 18,000 . They then have 180,000 - 18,000 = 162,000 employees

Next, Topconnect loses 120,000 * 5% = 120,000 * 0.05 = 6,000. They then have 120,000-6,000 = 114,000 employees

We can then add the customer amounts. Note that we are subtracting both sides before adding as both companies gain and lose customers simultaneously.

We can then add how much one company lost to the other company's customers.

Eyeconnect gains 6,000 customers, so they then have 162,000 + 6,000 = 168000 employees. Topconnect gains 18,000 customers so they then have 114,000 + 18,000 = 132,000 employees

b.

After many years, the number of customers Eyeconnect has will be less than the number of customers that Topconnect has. One way to find the end amount of customers that Eyeconnect has is to figure out when the customer bases even out, or when Eyeconnect loses the same amount of customers as Topconnect so the customer base stays the exact same. We know that no customers leave or join the companies except to leave/join the other, so the total amount of customers between the two companies stays the exact same. The amount of customers is 180,000 + 120,000 = 300,000. Therefore, at the end amount,

Eyeconnect customers (E) + Topconnect customers (T) =300,000

Furthermore, if the amount of customers that leave Eyeconnect is the same that leaves Topconnect, we can say

E * 0.1 = T * 0.05

divide both sides by 0.05 to isolate the T

E * 0.1 / 0.05 = T

2 * E = T

plug that into the first equation

E + 2 * E = 300,000

3 * E = 300,000

divide both sides by 3 to isolate E

E = 100,000 after many years

Answer:

D. 28

Step-by-step explanation:

Given:

m∠AFD = 90°

m∠AFB = 31°

Required:

m∠DFE

Solution:

m<AFB = m<CFD (both angles are marked as congruent angles)

Since m<AFB = 31°, therefore,

m<CFD = 31°

m<AFB + m<CFD + m<BFC = m<AFD

Plug in the known values

31° + 31° + m<BFC = 90°

62° + m<BFC = 90°

Subtract 62° from each side

m<BFC = 90° - 62°

m<BFC = 28°

m<BFC = m<DFE = 28° (both angles are marked congruent to each other)

Therefore,

m<DFE = 28°

Answer:

Horizontal Shift: Right 1

Vertical Shift: Down 5

Reflection: None

Explanation: To find the transformation, compare the function to the parent function (being in this case g(x)=1/x) and check to see if there is a horizontal or vertical shift or a reflection.

So, the answer would be Right 1, and down 5

Hope this helps you out :)

Answer:

9/49

Step-by-step explanation:

that is the procedure above

Answer:

1,000 defects

Step-by-step explanation:

Find how many defects that should be made by finding 1% of 100,000:

100,000(0.01)

= 1000

So, there should be 1,000 defects

Answer:

The 95% confidence interval for the mean of mid-upper arm circumference based on your sample is between 139.29 mm and 160.71 mm.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So

df = 4 - 1 = 3

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 3 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 3.1824

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 3.1824\frac{6.73}{\sqrt{4}} = 10.71[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 150 - 10.71 = 139.29 mm

The upper end of the interval is the sample mean added to M. So it is 150 + 10.71 = 160.71 mm

The 95% confidence interval for the mean of mid-upper arm circumference based on your sample is between 139.29 mm and 160.71 mm.

Answer:

A. 5

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Algebra II

Step-by-step explanation:

Step 1: Define

Identify points from graph.

Point (8, 5)

Point (4, 2)

Step 2: Find distance d

Simply plug in the 2 coordinates into the distance formula to find distance d

The LEAST selling price of the laptop should be ;

$1024.1 in other to avoid loss.

Price of laptop = $770

Tax = 20%

VAT = 13%

TO avoid loss ;

both the VAT percentage and TAX must be added to the price of the laptop:

Total percentage = VAT + TAX = (20 + 13) = 33%

THEREFORE, Least selling price should be :

Price of laptop * (1 + 33%)

770 * 1.33

= $1024.1

Learn more about TAX :

https://brainly.in/question/31818297

Explanation:

A = values on the die greater than 1

A = {2,3,4,5,6}

B = values on the die less than 5

B = {1,2,3,4}

Union those two sets together

C = A u B = {1,2,3,4,5,6}

Effectively, we get every possible value on the die. This is due to the "or" keyword. If it was "and", then it would be a difference story.

So the probability of getting anything in set C is 100% or just 1. We have guaranteed certainty we'll have this event happen.

( x + 1 )( x )( x - 5 ) =

( x + 1 )( x - 5 )( x ) =

( x^2 - 4x - 5 )( x ) =

x^3 - 4x^2 - 5x

Step-by-step explanation:

the other answer is basically correct.

as the simplest form you create 3 terms for the three given solutions (= the values for when the equation equals 0).

but maybe you need to add " = 0" for the full equation.

Answer:

-1/3

Step-by-step explanation:

Perpendicular lines have slopes that multiply to -1

a*b = -1

3 * b = -1

b = -1/3

The slope of line b is -1/3

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

Explanation:

You can use the AAS (angle angle side) theorem to prove that triangle ABD is congruent to triangle CBD.

From there, we can then say that AD and DC are the same length

AD = DC

3y+6 = 5y-18

3y-5y = -18-6

-2y = -24

y = (-24)/(-2)

y = 12

Answer:

The answer is that the runner can run 10 miles in 70 minutes.

Step-by-step explanation:

To solve for the number of miles that the runner can run in 70 minutes, start by setting up the information given from the problem in the form of a proportion.

A proportion is an equation which defines that the two given ratios are equivalent to each other. In other words, the proportion states the equality of the two fractions or the ratios. In a proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.

The proportion for this problem will look like [tex]\frac{2 miles}{14 minutes}=\frac{x}{70 minutes}[/tex]. (x) will be used as the variable for the number of miles that the runner can run in 70 minutes.  

To solve the proportion, start by cross multiplying to form an equation, and the equation will look like [tex](14)(x)=(2)(70)[/tex]. Next, simplify the equation, which will look like [tex](14)(x)=140[/tex]. Then, solve the equation by dividing both sides of the equation by 14, and it will look like [tex]x=10[/tex]. The final answer is that the runner can run 10 miles in 70 minutes.

Answer: The area is 22 17/64.

Step-by-step explanation:

base = 7 1/8 = 57/8

height = 6 1/4 = 25/4

area = 1/2*b*h

= 1/2*57/8*25/4

= 1425/64

= 22 17/64

9514 1404 393

Answer:

  13 < √181 < 14

Step-by-step explanation:

Apparently, you're supposed to know that ...

  13² = 169

  14² = 196

so √181 will lie between 13 and 14.

  13 < √181 < 14

Answer:

Option b, (4,2)

Option d, (8,4)

Option e, (12,6)

Answered by GAUTHMATH

Answer:

Option b, (4,2)

Option d, (8,4)

Option e, (12,6)

Step-by-step explanation:

the person above me is correct