Using the normal distribution and the central limit theorem, it is found that there is a 0.1913 = 19.13% probability that the sample mean for a sample of size 30 will be at least 99.
Normal Probability DistributionIn a normal distribution 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]
It 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, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].For the population, the mean and the standard deviation are given by, respectively, [tex]\mu = 95[/tex] and [tex]\sigma = 25[/tex].
For a sample of 30, we have that:
[tex]n = 30, s = \frac{25}{\sqrt{30}} = 4.6[/tex]
The probability that the sample mean for a sample of size 30 will be at least 99 is one subtracted by the p-value of Z when X = 99, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{99 - 95}{4.6}[/tex]
[tex]Z = 0.87[/tex]
[tex]Z = 0.87[/tex] has a p-value of 0.8078.
1 - 0.8087 = 0.1913.
0.1913 = 19.13% probability that the sample mean for a sample of size 30 will be at least 99.
More can be learned about the normal distribution and the central limit theorem at https://brainly.com/question/24663213
Help me with this question pleaseee
Answer:
< 1 = 26 degrees
< 2 = 154 degrees
< 3 = 26 degrees
< 4 = 26 degrees
< 5 = 154 degrees
< 6 = 154 degrees
< 7 = 26 degrees
Step-by-step explanation:
Because of angles opposed by the vertex, <2 = 154 degrees
Because of corresponding angles between parallel lines, <5 = <6 = <2 = 154 degrees.
Because of supplementary angles,
< 1 = < 3 = < 4 = < 7 = 180 - 154 = 26 degrees
Can someone please help, ty!!
(Will mark brainliest)
Answer:
Arcadia
Step-by-step explanation:
the line in the box is the median and Arcadia is bigger than Millersburg
Complete parts (a) and (b) below.
The number of dogs per household in a small town
Dogs
0
1
2.
3
Probability 0.650 0.216 0.087
0.026
4
5
0.014
0.009
(a) Find the mean, variance, and standard deviation of the probability distribution
Find the mean of the probability distribution
(Round to one decimal place as needed.)
Answer:
a) The mean of the probability distribution = 0.6
b) The variance of the probability distribution = 0.3
c) The standard deviation of the probability distribution = 0.5
Step-by-step explanation:
a) Data and Calculations:
number of dogs per household in a small town
Dogs Probability Expected Mean Diff Mean Diff.
Value Squared
0 0.650 0 -0.569 0.32376
1 0.216 0.216 -0.353 0.12461
2 0.087 0.174 -0.395 0.15603
3 0.026 0.078 -0.491 0.24108
4 0.014 0.056 -0.513 0.26317
5 0.009 0.045 -0.524 0.27458
The mean = 0.569 (Sum of expected value)
Variance = mean of squared differences = 0.27665 (1.38323/5)
Standard deviation = square root of variance = 0.526 = 0.5
The mean, variance and standard deviation of the considered probability distribution are evaluated to be:
Mean of the distribution = 0.569Variance of the distribution = 0.923 approxStandard deviation of the distribution = 0.96 approxHow to find the mean (expectation) and variance of a random variable?Supposing that the considered random variable is discrete, we get:
[tex]Mean = E(X) = \sum_{\forall x_i} f(x_i)x_i\\\\Variance = Var(X) = (\sum_{\forall x_i} f(x_i)x^2_i) - (E(X))^2\\[/tex]
As standard deviation is positive root of variance, thus,
[tex]\sigma = \sqrt {Var(X)}[/tex]
where [tex]x_i; \: \: i = 1,2, ... ,n[/tex] is its n data values
and [tex]f(x_i)[/tex] is the probability of [tex]X = x_i[/tex]
For this case, let we suppose that:
X = number of dogs per household in the considered town.
Then we have the probability distribution for values of X as:
Number of dogs Probability
0 0.650
1 0.216
2 0.087
3 0.026
4 0.014
5 0.009
Thus, we get:
Mean of X : E(X) = [tex]0 \times 0.650 + 1 \times 0.216 + 2 \times 0087 + 3 \times 0.026 + 4 \times 0.014 + 5 \times 0.009 = 0.569[/tex]
Variance of X:
Var(X) =
[tex](0^2 \times 0.650 + 1^2 \times 0.216 + 2^2 \times 0.087 + 3^2 \times 0.026 + 4^2 \times (0.014)\\ + 5^2 \times (0.009)) - (0.569)^2 \approx 0.923[/tex]
Standard deviation of X = [tex]\sigma = \sqrt {Var(X)} \approx \sqrt{0.923} \approx 0.96[/tex]
Thus, the mean, variance and standard deviation of the considered probability distribution are evaluated to be:
Mean of the distribution = 0.569Variance of the distribution = 0.923 approxStandard deviation of the distribution = 0.96 approxLearn more about expectation of a random variable here:
https://brainly.com/question/4515179
(2(3^2+1)^2÷(5^2×4÷2))^3÷2^4
Answer:
Step-by-step explanation:
Use PEDMAS
P - Parenthesis
Exponents
D - DIvision
M - Multiplication
A - Addition
S - Subtraction
[2 (3² + 1)² ÷ (5²*4÷2)]³÷ 2⁴ = [2 (9 + 1)² ÷ (25*4÷2)]³÷ 2⁴
= [2 (10)² ÷ (25*2) ]³÷ 2⁴
= [2*100 ÷ 50]³÷ 2⁴
= [2*2]³÷ 2⁴
= 4³÷ 2⁴
= 64 ÷ 16
= 4
how many real solutions does x²+8x+20=0 have?
Answer:
No real solutions
Step-by-step explanation:
Use the discriminant formula, D = b² - 4ac
D = b² - 4ac
Plug in b, a, and c:
D = b² - 4ac
D = (8)² - 4(1)(20)
D = 64 - 80
D = -16
Since the discriminant is negative, there are no real solutions
Since the solution is a complex value, hence the equation has no real solutions
Givne the quadratic expression x²+8x+20 = 0
Factorizing the function
x²+8x+20 = 0
x = -8±√8²-4(20)/2
x = -8±√64-80/2
x = -8±√-16/2
x = -8±4i/2
x = -4±2i
Since the solution is a complex value, hence the equation has no real solutions
Learn more on quadratic equations here:https://brainly.com/question/1214333
0.5 ft of snow melts to 2inches of H2o. To how many inches will 4.5 ft of snow melt?
Answer:
4.5 feet of snow = 27 inches H2o. Please read the explanation for better details
Step-by-step explanation:
if 0.5 feet of snow melts into 2 inches of water, then that means that 6 inches of snow melts into 2 inches of water. This means that for every 2 inches of snow you melt, it will become 1 inch of water. If 4.5 ft = 54 inches, you simply divide by 2, getting your answer of 27 inches of snow. Hope this helps! :)
Will mark brainliest:)
Answer:
Step-by-step explanation:
nice
2(2x + 3) = -4 + 2(2x + 5)
Answer:
All real numbers are solutions for this problem.
Step-by-step explanation:
You are most likely to encounter an irrational number when you are
Answer:
dealing with circles (using pi for circumference, area, arc angle, etc)
Answer:
Well, you can finding the area of a circle
Step-by-step explanation:
if a/3 = b/2 then what is the following ratio
a+b/5a
Answer:
1/3
Step-by-step explanation:
a=6
b=4
a+b=6+4=10
5.6=30
10/30=
1/3
I hope that it was helpful
~best wishes
Rob lost 77 pounds in the 1st 6 months of his diet then 16 pounds in the next 2 months find his average change in way each month
Answer:
7 is a good answer. Do you know how good of an answer 7 is. I don't think you do. If you don't know the answer always choose 7.
Ariel bought a 6-cup bag of dough for $6.34. She used 1.45 cups to make rolls and 3.45 cups to make bread. How much dough is left? PLEASE HEELP
Answer:
1.1 cups. Hope this helps.
Step-by-step explanation:
Please help me don’t know how to do it,
Answer:
7=60
6=60
5=120
4=120
2=60
1=120
Answer:
angle 4 and angle 5 is = 120degree
Step-by-step explanation:
A bird flies south. Its distance from its nest, as a function of time, is modeled by y=20x+1.
What statement best describes the function?
A. The function is linear at some points and nonlinear at others.
B. Not enough info to decide.
C. Linear
D. Nonlinear
Answer:
might be c
Step-by-step explanation:
intuition
Answer: c
Step-by-step explanation: the function is linear
(YOU WILL BE MARKED BRAINLIEST IF YOU WRITE A SHORT STORY FOR THIS MATH PROBLEM!!)
Write a short story that could represent this math problem.
Answer:
Once upon a time a troll was walking down a deep dark hallway, there was no light anywhere that he could see and he was starting to get scared of what could happen to him. But then out of the blue he saw something, something was would change his life forever, he saw a pigeon. Now you might think "Oh, a pigeon, how could that have changed his life?' Now the answer is kind of mundane but is deeper than you might think. The simple answer as to why the pigeon would change his life is because it gave the troll hope, hope that there is an exit. You see, the troll thought if the pigeon found there way into this pitch black hallway, then there must be a way in and hence a way out.
Now listen here, there's something that I wasn't telling you at the beginning of the story about the pigeon, the pigeon was also glowing. This is very useful obviously because it gave the troll some kind of light. Again, it gave the troll hope. Now, being a troll you might think that he would just snatch the pigeon and hold it for light, but this troll wasn't like other trolls, he had the capability to think before he used brute force to change something. So what the troll though was "If I just follow the pigeon then it might lead me to the exit because they have natural navigation in their brains"
Let's skip a while into the future, the troll followed and followed the pigeon for what felt like days, but in reality it was more like 3 hours. But then, the troll saw something that he thought he would never see again; sun light. As soon as the troll saw this, he started running and running towards the light, but as fast as he was running, the light seemed to get farther and farther away from him, then... POOF the troll was gone...
The troll found himself in a very lit up room, almost pure white all around him, which scorched his eyes because he was just in a pitch black room for hours. His ears were ringing and he was in pain, after a while all of that stopped, he was able to see clearly, he felt great, and his ears stopped ringing. What he saw was a very tall thin figure looking down at him from a room of pure white. The figure bent their neck and got right in the trolls face. The figure brought his left hand up to the trolls face, right next to his ear and snapped. The sound of a monstrous click sound right in the trolls ears hurt. The troll jumped back in fear but as soon as the click happened he saw a thing in his vision, a thing he new wasn't actually in the real world as it seemed to follow his eyes where ever he looked. It was, now i know this might sound stupid, I'm not here to imagine a story, I'm simply here to reenact the story of the troll. What he saw was a math problem, a grid was in his vision. It was a 4 by 6 grid.
The tall shadow figure was now back where the troll saw him originally, he was no longer bent and he seemed to not have arms anymore, just a tall dark figure with a cloak. The troll then began to hear a voice which seemed to come from everywhere. It was a deep voice that was very muffled, it said "Do this math problem and go back to your world. Get it correct and everything will go back to normal, but fail; and I'll have your soul" The troll was about to have an adventure of a lifetime...
Step-by-step explanation:
I legit came up with this on the spot, did you like it? XD
May I have brainliest please :)
Explain how the location of the vertex and the direction of the opening (upwards or downwards) affects the domain and range of the quadratic function. Use complete sentences.
Answer:
Following are the solution to this question:
Step-by-step explanation:
Its vertex position, as well as the position of its opening, influence its quadratic function set. Its y-coordinate of its vertex (v) and then all values of current above it are included in scope whenever the direction of openings becomes up therefore, the lowest y-value becomes possible.
It implies the scope is y >=v. If it sets up, then, y-coordinate of its vertex was its highest y value available, from all y-values above too y <= v. The scope of a quadratic function, as it will continue forever to left and right, from the negative to positive infinity.Rachel runs 3.2 miles each weekday and 1.5 miles each day of the weekend. How many miles will she have run in 6 weeks?
cloud is a vegetable grower, has 8 4/15 plots of pechay, 5 1/3 plots of eggplants and 5 2/5 of okra . how many plots of vetable do cloud has?
Answer:
The total plots of vegetable cloud will be: 19
Step-by-step explanation:
From the question statement, it is clear that the cloud has [tex]8\frac{4}{15}[/tex] plots of pechay, [tex]5\frac{1}{3}[/tex] plots of eggplants and [tex]5\frac{2}{5}[/tex] plots of okra.
so, Just add all the plots to get the total plots of the vegetable cloud.
i.e.
[tex]8\frac{4}{15}+5\frac{1}{3}+5\frac{2}{5}=\frac{124}{15}+\frac{16}{3}+\frac{27}{5}[/tex]
[tex]=\frac{124}{15}+\frac{80}{15}+\frac{81}{15}[/tex]
[tex]=\frac{124+80+81}{15}[/tex]
[tex]=19[/tex]
Therefore, the total plots of vegetable cloud will be: 19
A new company is hiring employees rapidly. Everyday the number of employees doubles in size. If it takes 48 days for the company to be at full capacity, how many days would it take for the company to be at half capacity?
Answer:
It would take the company 47 days to be at half capacity.
Step-by-step explanation:
From the question, it is stated that the number of employees doubles in size everyday. This implies that the current day capacity is equal to the previous day capacity. This can be written in a mathematical form as follows:
Current day capacity = Previous day capacity * 2 ......................... (1)
We can assume that the current day capacity which is 48th day in this question is equal to 100 employees. That is;
Current day capacity = 48th day capacity = 100
Substituting this into equation (1) above and solve for the previous day capacity, we have:
100 = Previous day capacity * 2
Previous day capacity = 100 / 2 = 50
Since 50 is half of 100 and the previous day is 47th day, it therefore implies that It would take the company 47 days to be at half capacity.
Select the correct answer. If 20% of a number is 35, what is 50% of that number?
Express in slope form
1. Evaluate 4x' + 7xy - 5y for x = 5, and y = 3.
Answer:
110 is your answer
Find the value of y in the given square. Only write the number value of y. *
1 point
Answer: y would =4 because the other answers if you plug in 9 with the X you will get 13 and when you plug 4 where the Y is you get 13
Step-by-step explanation:
Need help ASAP !!!!!!!!!!!!! Which statements describe the graph of f(x) = -1/4x as a transformation of the graph of g(x) = 1/x? Check all that apply.
A- the graph includes a vertical stretch.
B- the graph includes a compression.
C-the graph remains on the same side of the x-axis. D- the graph reflected across the x-axis ?
Answer:
It's B - The graph includes a compression
and D - The graph is reflected across the x-axis
Step-by-step explanation:
I got those right
B is right because f(ax) if a is greater than 1, then it includes a horizonal compression and 1/4x = f(4x)
D is right because -f(x) reflects across the x-axis. -f(x)= -1/x.
So -f(4x) = -1/4x
Answer:
b and d on edge
Step-by-step explanation:
just took the test
A paper company needs to ship paper to a large printing business. The paper will be
shipped in small boxes and large boxes. Each small box of paper weighs 45 pounds
and each large box of paper weighs 75 pounds. A total of 24 boxes of paper were
shipped weighing 1410 pounds altogether. Write a system of equations that could be
used to determine the number of small boxes shipped and the number of large boxes
shipped. Define the variables that you use to write the system.
HURRY AND ANSWER ILL GIVE 50 POINTS AND BRAINLIST! HOW YOU WORKED OUT THE PROBLEM MUST BE INCLUDED
ALL FOUR NEED TO BE DONE!
Answer:
Question #12: a. ⅛ b. ³/₂₀
Question #4: 9 ÷ 3 = 3
Question #5: a. 80½ yards² b. $1288.00
Question #9: 1½ inches
Question #8: 16/20
Step-by-step explanation:
I hope this helped!
Which table contains a set of non-linear ordered pairs?
Answer:
The second option is your answer
Step-by-step explanation:
The functions are not aligned here.
They are not even ordered in a function.
Your answer is the second option.
Answer: The bottom right graph
Step-by-step explanation: The increase in Y values is not consistent so the non-linear ordered pairs are in the bottom right graph.
Hope this helps!
Is this problem correct?
Answer:
Yes that is correct. B is correct.
Step-by-step explanation:
When you plug 0 in for x, the result is 3.
When you plug 1 in for x, the result becomes 1.
The equation matches up correctly.
f(x) = -2x + 3
#teamtrees #WAP (Water And Plant)
You got it right. Try to substitute x values in there to check your answer.
Here's an example
f(x) = -2x + 3
f(1) = -2(1) + 3 = -2+3 = 1
.
.
.
f(4) = -2 (4) + 3 = - 8 + 3= - 5
Keep up the good work!!
A particular fruitâs weights are normally distributed, with a mean of 598 grams and a standard deviation of 6 grams. The heaviest 8% of fruits weigh more than how many grams? Give your answer to the nearest gram.
Answer:
The 8% of the fruit weigh more than [tex]x=606.43 \ g[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 598 \ g[/tex]
The standard deviation is [tex]\sigma = 6 \ g[/tex]
Generally the 8% is mathematically represented as
[tex]P(X > x) = 0.08[/tex]
=> [tex]P(X > x) = P ( \frac{X - \mu}{\sigma }>\frac{x - 598}{6} )=0.08[/tex]
[tex]\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )[/tex]
[tex]P(X > x) = P ( Z >\frac{x - 598}{6} )=0.08[/tex]
From the normal distribution table the critical value corresponding area representing 0.08 towards the right tail of the curve is
[tex]z = 1.405[/tex]
So
[tex]\frac{x- 598}{6} = 1.405[/tex]
=> [tex]x=606.43 \ g[/tex]
!PLEASE HELP!
Find the value of x when the perimeter of a rectangle is 24 meters , the length = x + 3 meters and the width = 2x meters.?