Answer:
The 90th percentile for the distribution of the total contributions is $6,342,525.
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 normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes 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.
For sums of size n, the mean is [tex]\mu*n[/tex] and the standard deviation is [tex]s = \sqrt{n}*\sigma[/tex]
In this question:
[tex]n = 2025, \mu = 3125*2025 = 6328125, \sigma = \sqrt{2025}*250 = 11250[/tex]
The 90th percentile for the distribution of the total contributions
This is X when Z has a pvalue of 0.9. So it is X when Z = 1.28. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]1.28 = \frac{X - 6328125}{11250}[/tex]
[tex]X - 6328125 = 1.28*11250[/tex]
[tex]X = 6342525[/tex]
The 90th percentile for the distribution of the total contributions is $6,342,525.
What are the factors of 2x + 3x 54? Select two options
2x - 9
2x6
2x + 6
X-6
x+6
Answer:
(2x -9)(x +6)Step-by-step explanation:
Perhaps you're factoring ...
2x² +3x -54
= 2x² +12x -9x -54 . . . . rewrite 3x appropriately
= 2x(x +6) -9(x +6) . . . . factor pairs of terms
= (2x -9)(x +6) . . . . . . . . finish the factoring
The factors are (2x -9) and (x +6).
What’s the correct answer for this question?
Answer:
B.
Step-by-step explanation:
Volume of balloon = 4/3πr³
= 4/3(3.14)(0.5)³
= 0.52 cubic feet
Now
A helium tank contains 50 cubic feet of helium So,
Spherical balloons = 50/0.52
= 95.4
≈ 100
A company estimates that 0.8% of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of $400. If they offer a 2 year extended warranty for $27, what is the company's expected value of each warranty sold?
Answer:
The expected value of each warranty sold is $23.8.
Step-by-step explanation:
0.8% probability of the product failling.
If the product fails, the company will lose 400 - 27 = $373. So a net value of -373.
100 - 0.8 = 99.2% probability of the product not failling.
If the product does not fail, the company gains $27.
What is the company's expected value of each warranty sold?
We multiply each outcome by its probability.
0.008*(-373) + 0.992*27 = 23.8
The expected value of each warranty sold is $23.8.
Able, ben and cal each played a game.
able scored six times bens score.
cal scored a third of able's score. write down the ratio of able's score to ben;s score to cal's score
Answer:
Ratio of Able's score to Ben=6:1
Ratio of Ben's score to Cal's=1:2
Ratio of able's score to ben;s score to cal's score=6:1:2
Step-by-step explanation:
Let Ben's score =x
Able scored six times Ben's score
Able=6*x
=6x
Cal scored a third of Able's score
Cal=1/3 of 6x
=1/3(6x)
Ratio of Able's score to Ben
6x:x
=6:1
Ratio of Ben's score to Cal's score
x:1/3(6x)
=x:6x/3
=x:2x
=1:2
Ratio of able's score to ben;s score to cal's score=6:1:2
Given the following, determine the set (A'U B')∩C.
U = {x |x ∈ N and x < 10}
A = {x | x∈ N and x is odd and x < 10)
B = {x|x ∈ N and x is even and x < 10}
C = {x|∈E N and x < 8)
Answer:
n +10 =20
Step-by-step explanation:
answer =20 . thank God
A shop has 4 types of sweets (chocolate, taffy, gummies, and cookies), 2 types of snacks (chips and crackers), and 3 types of drinks (sodas, juice, and sports drinks).
Mystery boxes are put together that randomly combine 1 sweet, 1 snack, and 1 drink.
What is the probability that a mystery box contains chocolate, chips, and juice?
Answer:
1/24
Step-by-step explanation:
1/4*1/2*1/3 = 1/24
Find the constant of variation k for the direct variation 3x+5y=0
Answer:
-3/5
Step-by-step explanation:
3x+5y=0
Subtract 3x from each side
3x+5y-3x=0-3x
5y = -3x
Divide each side by 5
5y/5 = -3x/5
y = -3/5 x
A direct variation is y = kx
y = -3/5 x
The constant of variation is -3/5
What’s the correct answer for this question?
Answer:
C
Step-by-step explanation:
A cylinder is formed when rotating the 3-D figure around y-axis
PLEASE HELP IM STUCK ON A PROBLEM....
Answer:
Number line A.
Step-by-step explanation:
|-5x| - 11 = -1
Add 11 to both sides.
|-5x| = 10
-5x = 10 or -5x = -10
x = -2 or x = 2
Answer: Number line A.
1. An LG Dishwasher, which costs $800, has a 20% chance of needing to be replaced in the first 2 years of purchase. A two-year extended warrantee costs $112.10 on a dishwasher. What is the expected value of the extended warranty assuming it is replaced in the first 2 years?
2. Approximately 10% of all people are left-handed. Consider a grouping of fifteen (15) people.
a. State the random variable.
b. Write the probability distribution.
c. Draw a histogram.
d. Describe the shape of the histogram.
e. Find the mean.
f. Find the variance.
g. Find the standard deviation.
Step-by-step explanation:
The expected value of the extended warrant is calculated as follow.
Value of Waranty
= 800 x 20% − 112.10
= 800 x 20/100 − 112.10
= 47.9
The expected value of the extended warranty assuming it is replaced in the first 2 years is given as follow.
Expected value=800-112.10=>687.90
Therefore, required expected value of extended warranty is 687.90
2.
Given information:
Number of Trials (n) = 15
Probability of Success (p) = 0.10
a) Let X represents the number of left-handed people.
b) The probability distribution follows binomial distribution.
X ∼ Binomial distribution
The probability distribution is given as follow.
P(X = x) = ^nCx(p)^x(1 − p)^n − x
c)The histogram is given as follow. (See attachment)
d) The shape of histogram is skewed right.
e) The mean is calculated as follow.
Mean
=n x p
= 15 x 0.10
= 1.5
f) The variance is calculated as follow.
Variance
= n x p x q
= 15 x 0.10 x 0.90
= 1.35
g) The standard deviation is calculated as follow.
Standard deviation
=√n x p x q
=√15 x 0.10 x 0.90
= 1.162
Dorothy Kaatz, a computer programmer, earns a regular hourly rate of
$15.25 and earns double that when she works overtime. Kaatz usually works
40 regular hours and 12 hours overtime while she's trying to update the
company's systems before the month's end. What is her straight-time pay?
What is her overtime pay? What is her total pay?
Answer:
$976
Step-by-step explanation:
Straight time pay= $15.25(hourly rate) × 40(hours worked)= $610
Overtime Rate = 15.25×2= $30.50
Overtime Pay= $30.5 × 12 (Hours worked overtime)= $366
Total Pay= Basic wage + Overtime Wage = $976
Simplify the quotient shown 3480 divided by 29
Answer:
120
Step-by-step explanation:
3480/29=120
120
Simplify ———
1
final result is 120
What is the solution set up 7x^2+3X=0
Answer:
X=0,X=-3/7
Step-by-step explanation:
7x^2+3x=0
x(7x+3)=0
x=0
7x+3=0
7x=-3
x=-3/7.
Answer:-3/7
Step-by-step explanation:
Firstly add -3x to both sides of equation. 7x^2+3x-3x=0+-3x
7x^2=-3x
Divid both sides by X
7x^2/X=-3/X
7x=-3
Divid both sides by 7
7x/7=-3/7
X=-3/7
An option to buy a stock is priced at $150. If the stock closes above 30 next Thursday, the option will be worth $1000. If it closes below 20, the option will be worth nothing, and if it closes between 20 and 30, the option will be worth $200. A trader thinks there is a 50% chance that the stock will close in the 20-30 range, a 20% chance that it will close above 30, and a 30% chance that it will fall below 20.
Required:
a. Create a valid probability table.
b. How much should the trader expect to gain or lose?
c. Should the trader buy the stock? Explain.
Answer:
Step-by-step explanation:
An option to buy a stock is priced at $150. If the stock closes above 30 next Thursday, the option will be worth $1000. If it closes below 20, the option will be worth nothing, and if it closes between 20 and 30, the option will be worth $200. A trader thinks there is a 50% chance that the stock will close in the 20-30 range, a 20% chance that it will close above 30, and a 30% chance that it will fall below 20.
a) Let X represent the price of the option
x P(X=x)
$1000 20/100 = 0.2
$200 50/100 = 0.5
$0 30/100 = 0.3
b) Expected option price
[tex]= \sum x.P(X=x)\\\\ = 1000 * 0.2 + 200 * 0.5 + 0 = \$ 300[/tex]
Therefore expected gain = $300 - $150 = $150
c) The trader should buy the stock. Since there is an positive expected gain($150) in trading that stock option.
The speed of a passenger train is 6 mph faster than the speed of a freight train. The passenger train travels 260 miles in the same time it takes the freight train to travel 230 miles. Find the speed of each train.
Step-by-step explanation:
let speed of freight train be x
speed of passenger train = x+6
Passenger train distance = 280 miles
freight train 250 milesthe times taken for these distances is the same
280/(x+6)=250/x
280x=250(x+6)
280x=250x+1500
30x = 1500
x= 50 mph the speed of freight train.
x+6= 50+6 = 56mph = speed of passenger train.
Assume that 1100 births are randomly selected and exactly 556 of the births are girls. Use subjective judgment to determine whether the given outcome is unlikely, and also determine whether it is unusual in the sense that the result is far from what is typically expected.
Answer:
The sample proportion for the births that are girls is 0.505. It is slightly higher than the expected value of 0.5, but the right way to answer if it is an unusual proportion is by performing an hypothesis test.
The hypothesis test results in not enough evidence to claim that the outcome is unlikely. This sample result has a probability of 0.7627 of appearing by pure chance in a population with proportion p=0.5.
Step-by-step explanation:
This is a hypothesis test for a proportion.
The claim is that the proportion of girls birth differs significantly from the expected proportion (50%).
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.5\\\\H_a:\pi\neq 0.5[/tex]
The significance level is 0.05.
The sample has a size n=1100.
The sample proportion is p=0.505.
p=X/n=556/1100=0.505
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.5*0.5}{1100}}\\\\\\ \sigma_p=\sqrt{0.000227}=0.015[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.505-0.5-0.5/1100}{0.015}=\dfrac{0.005}{0.015}=0.302[/tex]
This test is a two-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=2\cdot P(z>0.302)=0.7627[/tex]
As the P-value (0.7627) is greater than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the proportion of girls birth differs significantly from the expected proportion (50%).
Which linear function has initial value 4?
a. y = 3x - 4
b. y = - 3x + 4
c. y = 4x - 3
d. y = 4x + 3
Answer:
y = -3x+4
Step-by-step explanation:
An initial value of 4 would be the y intercept
The only function with a y intercept of 4
(y = mx+b where b is the y intercept)
is y = -3x+4
If the captain has a 3/4 probability of hitting the ship and the pirate has a 1/4 probably what is the probability the pirate hits and the captain misses
Answer:
9/16
Step-by-step explanation:
captain has a 3/4 probability of hitting the ship
pirate has a 1/4 probability of hitting the ship
This means he has a 3/4 probability of missing the ship
P (captain hitting and pirate missing) = 3/4*3/4 = 9/16
Electricity usage data consists of 45 months has a mean number of units consumed is 390.47 per month with a standard deviation of 170.5 units per month. Assume that the number of units consumed are approximately normally distributed. Estimate 95% confidence interval for the average monthly electricity consumed units.
Answer:
The 95% confidence interval for the average monthly electricity consumed units is between 47.07 and 733.87
Step-by-step explanation:
We have the standard deviation for the sample. So we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 45 - 1 = 44
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 44 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.0141
The margin of error is:
M = T*s = 2.0141*170.5 = 343.4
In which s is the standard deviation of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 390.47 - 343.40 = 47.07 units per month
The upper end of the interval is the sample mean added to M. So it is 390.47 + 343.40 = 733.87 units per month
The 95% confidence interval for the average monthly electricity consumed units is between 47.07 and 733.87
Fiad the sample variance and standard deviation.
21, 10, 3, 7, 11
Answer:
SD = 5.987, Var(X) = 35.85
Step-by-step explanation:
Apply the standard deviation formula, remembering that n represents the sample size. Then, just take the square of the standard deviation to obtain the variance.
Hope this helps!
Please answer this correctly
Answer:
3 3/5 hours.
Step-by-step explanation:
There are 3 students who logged 1 1/5 so:
[tex]1\frac{1}{5} +1\frac{1}{5} +1\frac{1}{5} =3\frac{3}{5}[/tex]
3 3/5 hours have been logged total by those who logged 1 1/5 hours.
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
D. Time ( length)
Step-by-step explanation:
The function is measuring the length of the race, and the time it took to complete. So, it would be D.
// have a great day //
Answer:
D. Time(length)
Step-by-step explanation:
→The time is on the outside because, according to the information that has been given/provided, the length of the race depends on the time taken to complete the race.
This means the correct answer is "D. Time(length)."
If an exponential model was used to fit the data set below, which of the following would be the best prediction for the output of the model if the input was x=20?
Answer:
The equation is found to be: [tex]y = 50.6e^{0.16x}[/tex]
y(20) = 1241.34
Step-by-step explanation:
The given data is:
x: 3 7 11 14 17
y: 83 142 301 450 722
Now, we find sum summation values, relevant to the formula of exponential regression model, using calculator:
∑ ln y = 27.77305, ∑x ln y = 308.1494, ∑x = 52, ∑ x² = 664
and, n = no. of data points = 5
Now, we use formulae of exponential regression model to find out values of constant:
b = (n∑x lny - ∑x ∑ln y)/[n∑x² - (∑x)²]
b = [(5)(308.1494) - (52)(27.77305)]/[(5)(664) - (52)²]
b = 0.16
Now, for a;
a = (∑ln y - b∑x)/n
Therefore,
a = [(27.77305) - (0.16)(52)]/5
a = 3.9
For, α:
α = e^a = e^3.9
α = 50.6
So, the final equation of exponential regression model is given as:
[tex]y = \alpha e^{bx}\\ y = 50.6e^{0.16x}[/tex]
Now, we find value of y for x = 20:
y(20) = (50.6) e^(0.16*20)
y(20) = 1241.34
Graph the line that represents this equation. 3x - 4y =8
Answer:
See attachment
Step-by-step explanation:
The solution is given in the image.
Which graph is the graph of the function?The graph of a feature f is the set of all factors in the plane of the form (x, f(x)). We can also outline the graph of f to be the graph of the equation y = f(x). So, the graph of a feature is a special case of the graph of an equation.
What does the axis of a graph constitute?An axis is a line to the aspect or backside of a graph; it's far labeled to give an explanation for the graph's meaning and the devices of measurement. The x-axis, the horizontal line at the lowest of a graph, may be labeled to present facts about what the graph represents.
Learn more about graphs here: brainly.com/question/4025726
#SPJ2
Accident rate data y1, ...., y12 were collected over 12 consecutive years t=1,2,...12. At over 12 consecutive years t = 1,2,..., 12. At the end of the 6th year, a change in safety regulations occured. FOr each of the following situations, set up a linear model of the form y=XB+E. Define X and B appropriately.
a. The accident rate y is a linear function of t with the new safety regulations having no effect.
b. The accident rate y is a quadratic function of t with the new regulations having no effect.
c. The accident rate y is a linear function of t. The slope for t>= 7 is the same as for t<7. However there is a discrete jump for t=7.
d. The accident rate y is a linear function of t. After t=7, the slope changes, with the two lines intersecting at t=7.
Answer:
The correct option is;
The accident rate is a linear model function of t. After t = 7, the slope changes, with the two lines intersecting at t = 7
Step-by-step explanation:
The given parameters are;
Accident rate data = y₁, y₂, y₃, y₄, y₅, y₆, y₇, y₈, y₉, y₁₀, y₁₁, y₁₂
Time at which data was recorded = t₁, t₂, t₃, t₄, t₅, t₆, t₇, t₈, t₉, t₁₀, t₁₁, t₁₂
Accident rate equation is a linear model given as follows;
y = X·B + E
Where:
y = Accident rate
X = Slope of linear model
B = Year
E = y intercept of model
At the end of the 6th year, a change in a regulation that affects safety, hence accident rate occurred given as follows;
Before the change in safety regulations occurred for year t < 7 y₁ = X₁B + E₁
After the change in safety regulations occurred for year t < 7 y₂ = X₂B + E₂
Therefore the slope changes from X₁ to X₂ after t = 7 with the second linear model starting from the end of the first linear model making the two lines intersect at t = 7 (the beginning of year 7)
Hence the correct option is that "The accident rate is a linear model function of t. After t = 7, the slope changes, with the two lines intersecting at t = 7."
math question is attached below
and show your work
Answer:
[tex]V = \frac13 \pi r^2 h[/tex]
117.81
Step-by-step explanation:
r is half the diameter so 2.5 cm
h is 18
fill in and get:
V = [tex]\frac13 \pi \cdot 6.25 \cdot 18 \approx 117.81 cm^3[/tex]
I earn $12.00 in 5 hours. At this rate, how many hours will it take to earn $19.20?
Answer:
8 hours
Step-by-step explanation:
Solve with a proportion
[tex]\frac{12}{5}[/tex] = [tex]\frac{19.20}{x}[/tex]
Multiply 5 by 1.6 to get x
5 x 1.6 = 8
SOMEONE PLEASE HELP ME ASAP PLEASE!!!
Answer:
3.6
Step-by-step explanation:
d = sqrt(3^2+2^2) = sqrt(13) = 3.6
Question 1 of 20 :
Select the best answer for the question.
1. Divide7/15 by 3/5
OA%
O B./25
O c. 75/21
O D.21/75
Answer:
7/9
Step-by-step explanation:
7/15 ÷ 3/5
Copy dot flip
7/15 * 5/3
7/3 * 5/15
7/3 * 1/3
7/9
TIVITY MODULE
The length of a rectangle is eight centimeter less than
twice the width. The area of the rectangle is 24
centimeters squared. Determine the dimensions of the
rectangle in centimeters.
Answer: Length: 4, width: 6
Step-by-step explanation:
Let the length be x and width be y
Then x=2y-8 and xy=24
Substitute to get 2y-8 * y = 24, so 2y^2-8y=24 or y^2-4y=12, then solve to get y=6 or y=-2. Since width is positive y=6.
Substitute y=6 into xy=24 to get x=4.
Length: 4, width: 6
Hope that helped,
-sirswagger21
