Answer:
0.0027 = 0.27% probability that the sample mean of non-interscholastics is greater than the sample mean of interscholastic athletes
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution, the central limit theorem, and subtraction of normal variables.
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.
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
At a large state university, the heights of male students who are interscholastic athletes is approximately Normally distributed with a mean of 74.3 inches and a standard deviation of 3.5 inches. Sample of 10:
This means that [tex]\mu_I = 74.3, s_I = \frac{3.5}{\sqrt{10}}[/tex]
Those who are "non-interscholastics" have mean of 70.3 inches and a standard deviation of 3.2 inches. Sample of 12.
This means that [tex]\mu_N = 70.3, s_N = \frac{3.2}{\sqrt{12}}[/tex]
What is the probability that the sample mean of non-interscholastics is greater than the sample mean of interscholastic athletes?
This is the probability that:
N - I > 0
Distribution N - I:
[tex]\mu = \mu_N - \mu_I = 70.3 - 74.3 = -4[/tex]
[tex]s = \sqrt{s_I^2+s_N^2} = \sqrt{(\frac{3.5}{\sqrt{10}})^2+(\frac{3.2}{\sqrt{12}})^2} = 1.44[/tex]
Probability:
One subtracted by the p-value of Z when X = 0.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0 - (-4)}{1.44}[/tex]
[tex]Z = 2.78[/tex]
[tex]Z = 2.78[/tex] has a p-value of 0.9973
1 - 0.9973 = 0.0027
0.0027 = 0.27% probability that the sample mean of non-interscholastics is greater than the sample mean of interscholastic athletes
The probability for the sample mean of non-interscholastics is greater than the sample mean of interscholastic athletes in state university is 0.0027.
What is normally distributed data?Normally distributed data is the distribution of probability which is symmetric about the mean.
The mean of the data is the average value of the given data. The standard deviation of the data is the half of the difference of the highest value and mean of the data set.
At a large state university, the heights of male students who are interscholastic athletes is approximately Normally distributed with a mean of 74.3 inches and a standard deviation of 3.5 inches. The heights of male students who don't play interscholastic sports is approximately Normally distributed with a mean of 70.3 inches and a standard deviation of 3.2 inches.For the above data, the value of mean would be
[tex]m=70.3-74.3\\m=-4[/tex]
The selected sample size are 10 interscholastic athletes and 12 non-interscholastics. The value of standard deviation is,
[tex]\sigma=\sqrt{(\dfrac{3.5}{\sqrt{10}})^2+(\dfrac{3.2}{\sqrt{10}})^2}\\\sigma=1.44[/tex]
The Z score can be find out using the following formula.
[tex]Z=\dfrac{X-\mu}{\sigma}\\Z=\dfrac{0-(-4)}{1.44}\\Z=2.78[/tex]
The z score of 2.78 has the p value equal to 0.9973. For sample mean of non-interscholastics to be greater, the probability,
[tex]P=1-0.9973\\P=0.0027[/tex]
Thus, the probability for the sample mean of non-interscholastics is greater than the sample mean of interscholastic athletes in state university is 0.0027.
Learn more about the normally distributed data here;
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Find the volume and show work
Answer:
Volume = 2512 km³
Volume = 800π km³
Step-by-step explanation:
Volume Cylinder = Area circle * height
Let's input the info
Formula for the Area of a circle = πr²
Area circle = π*100
Since it asks to leave in terms of π or tenths ill give both.
Area circle = 100π
Area circle = 314
Volume = 100π * 8
Volume = 800π
Volume = 314 * 8
Volume = 2512
Units = km³
Volume = 800π km³
Volume = 2512 km³
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
a triangle has vertices r(1,2), s(3,3) and t(-3,4)
Give The Rest of the question
Answer:
Reflection about x axis
r(1,2)-----------r'(1,-2)
, s(3,3) ..........s'(3,-3)
and t(-3,4).....t'(-3,-4)
Carol creates a flag consisting of two similar triangles and labels them
A ABC and A XYZ. Side AB is 5 cm and side XY is 15 cm. If the perimeter of A
ABC is 16 cm, what is the perimeter of A XYZ ?
A) 26 cm
B) 6cm
C)48cm
D)144cm
Answer: 48
Step-by-step explanation:
Andre has seven dollars he needs $50 to buy a skateboard each week his grandmother pays him four dollars to complete some chores how much money does Andre have after the week
Answer:
$11
$39
Step-by-step explanation:
Amount Andre has = $7
Amount his grandmother pays him every week = $4
Amount Andre needs to buy a skateboard = $50
how much money does Andre have after the week?
Amount of money Andre has after the week = Amount Andre has + Amount his grandmother pays him every week
= $7 + $4
= $11
Amount of money Andre has after the week = $11
Amount Andre needs more to buy the skateboard = Cost of the skateboard - Amount of money Andre has after the week
= $50 - $11
= $39
Amount Andre needs more to buy the skateboard = $39
please help me, due tomorrow!!!
Answer:
1. B
Step-by-step explanation:
the only 1 i could do is number 1 which i dont even think it is correct
The area of a rectangle is 8 square yards.
What is the area of the same rectangle when measured in square feet?
Answer:
24 square feet
Step-by-step explanation:
If the area of the rectangle is square yards then the area in feet would be 24 because there are 3 feet in a yard my multiply 8*3 to get 24.
Answer:
72
Step-by-step explanation:
Guy above was so wrong its 72 square feet I did the test
Wendy noticed that out of 345 cars that passed by her house 56 were SUVs. About how many SUVs could she expect to see pass by if 2,100 cars were to pass her house?
Answer:
341 SUVs
Step-by-step explanation:
56/345*2100= 7840/23 or around 341 SUVs
Hope this helped! :)
Katelyn invested $1500 into her account which earned interest compounded continuously. After 10 years, she discovered that she had $3935.36. What interest rate percent did Katelyn earn?
Answer: ____ % interest
Given:
Principal = $1500
Time = 10 year
Amount after interest compounded continuously = $3935.36
To find:
The rate of interest.
Solution:
The formula for amount after continuous compound interest is:
[tex]A=Pe^{rt}[/tex]
Where, P is principal, r is the rate of interest in decimal and t is time in years.
Putting [tex]P=1500,A=3935.36,t=10[/tex] in the above formula, we get
[tex]3935.36=1500e^{r(10)}[/tex]
[tex]\dfrac{3935.36}{1500}=e^{10r}[/tex]
[tex]2.6236=e^{10r}[/tex]
Taking ln on both sides, we get
[tex]\ln(2.6236)=\ln e^{10r}[/tex]
[tex]0.9645=10r[/tex] [tex][\because \ln e^x=x][/tex]
Divide both sides by 10.
[tex]\dfrac{0.9645}{10}=r[/tex]
[tex]0.09645=r[/tex]
The rate of interest in percentage is:
[tex]r=100\times 0.09645[/tex]
[tex]r=9.645\%[/tex]
Therefore, the required rate of interest is 9.645%.
i need helpp please this is due today (show work/explanation)
Answer:
14 x 14 = 196
10 x 14 x 1/2(basically just dividing by 2) = 70
70 x 4(four sides of triangles) = 280
Now let's add the areas together:
196 + 280 = 476 cm^2 is your answer.
DESPERATE, PLEASE ANSWER FAST
(multiple choice answer)
Which associations best describe the scatter plot?
Select each correct answer.
Linear association
Nonlinear association
Negative association
Positive association
Answer:
Nonlinear association
Step-by-step explanation:
Re-write the quadratic function belbw in Standard Form
y = 3(x - 3)(x - 2)
Answer:
y = 3x² - 15x + 18
Step-by-step explanation:
y = 3(x - 3)(x - 2) ← expand factors using FOIL
= 3(x² - 5x + 6) ← distribute parenthesis by 3
y = 3x² - 15x + 18 ← in standard form
ANSWER
SEE EXPLANATION
Step-by-step explanation:
3(x²-2x-3x+6)
3(x²-5x+6)
3x²-15x+18
Mary would like to save $10 000 at the end of 5 years for a future down payment on a car
a) How much should she deposit at the end of each month in a savings account that pays 1.2%/a, compounded monthly, to meet her goal?
b) If you currently have a part-time job, consider your hourly wage. If you do not have a job, use the minimum hourly wage in your jurisdiction. How many hours each month would you have to work, just to make those payments? Write a brief reflection on the advantages and disadvantages to long-term saving for a purchase, compared to borrowing a large sum of money and paying it off over time. Note that interest rates for savings accounts are always lower than interest rates for borrowing!
Answer:
a) $161.8
b i) Approximately 327.7 hours
ii) The cost of saving is less but the opportunity cost of saving can be higher with regards to technology and regulation
Step-by-step explanation:
The amount Mary would like to save, FV = $10,000
The time Mary over which Mary intends to save the amount, t = 5 years
Therefore, the number of monthly payments, n = 12
a) The amount in interest the bank pays compounding, i = 1.2% per annum
The amount that Mary will deposit each month is given as follows;
The compound interest formula is given as follows;
[tex]PMT = \dfrac{FV}{\left (\dfrac{ \left (1 + \dfrac{i}{12} \right )^n - 1}{ \dfrac{i}{12}} \right)}[/tex]
Where;
PMT = The monthly payment
Therefore, we get;
[tex]PMT = \dfrac{10,000}{\left (\dfrac{ \left (1 + \dfrac{0.012}{12} \right )^{60} - 1}{ \dfrac{0.012}{12}} \right)} \approx 161.8[/tex]
PMT = 10,000/((1 + 0.012/12)^(60) - 1)/(0.012/12)) ≈ 161.8
The amount she needs to deposit monthly, PMT ≈ $161.8
b i) Given that the minimum wage varies and we have a minimum wage here is officially approximately $79, which is 160 hours a month work
The number of hours work needed = 161.8/79 × 160 ≈ 327.7 hours a month approximately
b ii) Given that the interest rate for saving is lower than the interest rate for borrowing, the amount paid by saving is much lesser than the amount paid back when borrowing, therefore, it is more cost effective to save
However, while saving, changes may take place, such as the use of what is being saved for, therefore, it can be more beneficial to borrow and make use of the items now while they are still available and acceptable, such as the drive towards net zero is making fuel based cars less popular with the drive being towards electric cars.
A) y=1/3x-8
B) y=1/3x-4
C) y=1/3x+2
D) y=1/3x-14
Answer:
A
Step-by-step explanation:
Concept :-
The slope intercept form of a line is y = mx + c Where m is slope , and c is constant .On converting :-
[tex]\bf\implies y + 5 =\dfrac{1}{3}(x-9)\\\\\bf\implies y + 5 =\dfrac{1}{3}x - 3 \\\\\bf\implies y = \dfrac{1}{3}x - 3 - 5 \\\\\bf\implies\boxed{\red{y = \dfrac{1}{3}x -8 }}[/tex]
Hence option A is correct.Help what’s the answer ?
Answer:
-5x+13
Step-by-step explanation:
-2x+9-3x+4
=-5x+13
help!!!!!!!!! i am really confused and need help
Answer:
g(-3)= -3^3-7
= -27-7
= -34
solve for x. and please explain your answer
Use the figure below to determine the length of sides b and c.
Question 5 options:
b = 5√3, c = 10
b =10, c = 5√3
b = 5√2, c = 10√3
b = 5, c = 10√2
Answer:
Option A
The value of the length of sides b and c is 5√3 and
10 respectively.
Step-by-step explanation:
Here, a given figure
Let the ΔABC
m∠B = 90°, m∠C = 30°, AB = 5, BC = b, AC = c
Now,
Sin θ = O/H
Sin 30° = 5/c
1/2 = 5/c
1 × c = 5 × 2
c = 10
Then,
tan θ = O/A
tan 30° = 5/b
1/√3 = 5/b
b × 1 = 5 × √3
b = 5√3
Thus, The value of the length of sides b and c is 5√3 and
10 respectively.
-TheUnknownScientist
Question
Am I going to past science class and not go to summer school?
Answer:
yes u got this shawty
Step-by-step explanation:
A computer can perform 4.66 x 10 exponent 8 calculations per second. How many calculations can this computer perform in one minute
Answer:
2.796x10^10
Step-by-step explanation:
4.66x10^8 in one second
1 minute is equal to 60 seconds
Multiply 4.66x10^8 by 60
= 2.796x10^10
Marulla's z score on a college entrance exam is 1.3. If the raw scores have a mean of 480 and a standard deviation of 70 points, what is her raw score?
Answer:
571
Step-by-step explanation:
We solve using z score.
z = (x-μ)/σ, where
x is the raw score = ?
μ is the population mean = 480
σ is the population standard deviation = 70
z = 1.3
Hence,
= 1.3 = x - 480/70
Cross Mulitiply
1.3 × 70 = x - 480
91 = x - 480
x = 480 + 91
x = 571
Therefore, Marulla's raw score is 571
Malcom is filling bags with rice. He starts with 5 1/4 lbs. container of rice and fills each bag with 5/8 pound of rice. How many bags can Malcom fill?
Express your answer in scientific notation. 8.8*10^7+3.1*10^8
Answer:
i can't explain how but the answer is:
3.98 * 10^8
Answer:
39.8 x 10^7
Step-by-step explanation:
Factor the expression
(8.8+3.1x10) x 10^7
Multiply
(8.8+31) x 10^7
Add
39.8 x 10^7
Hope this helps! If you need any other help lmk! :)
Mai put $4,250 in the bank for a rate of 4% simple interest per year. After
3 years, what will be the balance of her bank account?
0
Answer:
4760
Step-by-step explanation:
Simple interest formula:
PV(1+it)
4250(1+.04*3)=4760
A square is rotated clockwise about center point P.
Click on all the degrees of rotation that will carry the square onto itself,
45
900
120
135
180
225
240
270
315
360
The degrees of rotation that will carry the square onto itself are,
⇒ 90°, 180°, 270°, 360°
Since, A Square is a two dimension figure with 4 sides, 4 corners and 4 right angles. All the sides of the square are equal and parallel to each other.
Given here:
A square is rotated clockwise about center point P.
Now , Since there are have 4 vertices, your starting vertex can land in 4 different starting places and still come up with the same figure.
So if you take 360/4 you get 90 degree rotations to each consecutive vertex.
or more specifically;
= 360/4
= 90
Hence, the square will coincide itself after every integral multiple of 90.
Thus, 90°, 180°, 270°, 360° are the required angles of rotation.
Learn more about the rectangle visit:
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In parallelogram MNPQ if QR=5 find RN.
Answer:
RN=5
Step-by-step explanation:
QR is congruent to RN therefore they are the same length
Santos flipped a coin 300 times. The coin landed heads up 125 times. Find the ratio of heads to total number of coin flips. Express as a simplified ratio. Answers:
A- 5 to 12
B- 7 to 12
C- 12 to 5
D- 5 to 7
Answer:
5/12
Step-by-step explanation:
No. of times coin landed head up / Total no. of flips
= 125 / 300
= 25*5 / 25*12
= 5 / 12
How many square feet of outdoor carpet will we need for this hole
Answer: multiply the numbers
Step-by-step explanation:
try multiplying the numbers
f(x)=2x2−10x+11 What is f(4)?
Set the polynomial equal to y y to find the properties of the parabola. y=2x2+10x+11 y = 2 x 2 + 10 x + 11. Rewrite the equation in vertex form. Tap for more steps.
help please!! if it’s correct ill mark you as brainliest
Answer:
[tex]\frac{2\pi }{25}[/tex]
(8^2 x pi)/ (20x40)
When 5x^2−5 is completely factored, which is one of its factors?
Answer:
no, never completely factored with negative exponents
Step-by-step explanation:
5x^-3 = 5/x^3