Answer:
0.7517 = 75.17% probability that the mean IQ of the 3 North Catalina students is at least 5 points higher than the mean IQ of the 3 Chapel Mountain students
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.
Subtraction of normal variables:
When we subtract normal variables, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.
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.
North Catalina:
Population has mean 130 and standard deviation 8 points. Sample of 3. This means that:
[tex]\mu_{N} = 130, s_{N} = \frac{8}{\sqrt{3}} = 4.6188[/tex]
Chapel Mountain:
Population has mean 120 and standard deviation 10 points. Sample of 3. This means that:
[tex]\mu_{C} = 120, s_{C} = \frac{10}{\sqrt{3}} = 5.7735[/tex]
What is the probability that the mean IQ of the 3 North Catalina students is at least 5 points higher than the mean IQ of the 3 Chapel Mountain students?
We want that: [tex]N - C > 5[/tex]
Distribution N - C:
The mean is:
[tex]\mu = \mu_N - \mu_C = 130 - 120 = 10[/tex]
The standard deviation is:
[tex]s = \sqrt{s_N^2+s_C^2} = \sqrt{4.6188^2+5.7735^2} = 7.3937[/tex]
This probability is 1 subtracted by the pvalue of Z when X = 5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{5 - 10}{7.3937}[/tex]
[tex]Z = -0.68[/tex]
[tex]Z = -0.68[/tex] has a pvalue of 0.2483
1 - 0.2483 = 0.7517
0.7517 = 75.17% probability that the mean IQ of the 3 North Catalina students is at least 5 points higher than the mean IQ of the 3 Chapel Mountain students
6x+12 in its simplest form?
Answer:
It is already in simplest form.
Step-by-step explanation:
Answer:
Already in simplest form
Step-by-step explanation:
I mean you could do 6(x+2) but its already in its simplest form.
The graph of a line and and exponential intersect twice, once, or not at all. Describe the possible number of intersections of each of the following pairs of graph. Your solution to each part should include all of the possibilities and a quickly sketched example of each one. (Part 1)(SHOW WORK)
a. A line and a parabola
b. Two different parabolas
a) A line can intersect a parabola at 2 points, 1 point, or no points respectively. The only possible way at which it intersects at 1 point, would be if it were tangent to the parabola. [Check first attachment]
b) Two different parabolas can intersect at 2 points, 1 point or no points respectively. [Check second attachment]
It is possible for 2 parabolas to intersect at 4 and even 3 points. But one of the parabolas would be on it's side. You can consider those cases.
When f ( x ) = 9 x 2 + x − 5 , evaluate f ( − 4
Answer:
is that supposed to be a squared x?
9(-4)^2 + (-4) - 5 = 135
9(-4) × 2 + (-4) - 5 = -81
id.k which one is right sorry
If one-fourth of 2^30 is equal to 2^x, what is x?
Answer:
28
Step-by-step explanation:
1/4 can be rewritten as 1 / (2^2)
or 2^-2.
using the 2nd form,
we have 2^-2 * 2^30 = 2^x
By exponent rule
2^28 = 2^x
So we can observe now that x = 28
Answer:
23
Step-by-step explanation:
The table below shows Greg's scores at a state golf tournament. What is Greg's
average score for the five rounds?
A. -4
B. -3
C. -2
D. -1
Answer: d
Step-by-step explanation:
You add all of his scores up and divide them by how many numbers there are which 3+1+ -3+ -2+ -4 equals -5 and you divide them by the five numbers which gives you one
Please help I need it
Answer:
A. Yeah
Step-by-step explanation:
Question 7 (3 points) Write this decimal division as equivalent whole number division. 19.05 ÷ 1.5 = ÷ Find the quotient.
Answer:
~12.7~
Step-by-step explanation:
hope this helps brainlest!
Use the figure to find the measures of the numbered angles.
Answer:
1 = 81 degrees
2 = 99 degrees
3 = 81 degrees
4 = 99 degrees
5 = 81 degrees
6 = 99 degrees
7 = 81 degrees
Answer:
Step-by-step explanation:
1 = 81 degrees
2 = 99 degrees
3 = 81 degrees
4 = 99 degrees
5 = 81 degrees
6 = 99 degrees
7 = 81 degrees
plz help asap!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
a 12/20 = 0.6
b 21/35 = 0.6
c 28.8/48 = 0.6
pleeeaassee First person get brainliest!!!!
Answer:
D. 32 inches 65-33=32 so its 32 inches
Step-by-step explanation:
The following expression represents the profit made by John as he mows
lawns: P = 20L - 100
Which description correctly interprets each part of the expression?
Answer:
P is price per lawn, 20 is the money made per lawn, L is the number of lawns mowed, 100 is his initial cost.
Step-by-step explanation:
calculate the volume of a liquid with a density of 5.45g/km and a mass of 65g
Answer:
11.93 ml
rounded to two significant figures: 12ml
Step-by-step explanation:
65/5.45=11.93 ml
Please mark me as brainliest
Of the pets in the pet show, 10/12 are cats. 6/10 of the cats are calico cats. What fraction of the cats are calico cats?
Answer:
6/10, simplified 3/5
Step-by-step explanation:
kinda tricky, but the fraction is stated right out.
Answer:
3/5
Step-by-step explanation:
a patients dose of medication increased from 100mg to 150mg. What is the percent increase in medication?
Answer:
The answer is 50% increase. Hope this helped!
Step-by-step explanation:
Help please plzzzzzzzz
Answer:
60
Step-by-step explanation:
120 + 90 + 90 + 60 = 360
1. Observa el siguiente conjunto de enteros (-1,0, 1)
A. ¿Cuál de las propiedades de los números reales son verdaderas
para el conjunto?
Answer:
no hablo espanol papas fritas papas fritas papas fritas papas fritas papas fritas papas fritas papas fritas papas fritas
Step-by-step explanation:
True or false?is the point(16,4) included in this function: Y=2x or Y=x2 or y= x+12 or y=x-12
Answer:
True
Step-by-step explanation:
It is true because the graph of [tex]y=x-12[/tex] passes through the point [tex](16,4)[/tex]
x = 16
y = 4
Substitute
4 = 16 - 12
4 = 4
Therefore, the answer is true.
Which statement about the ordered pair (-6,8) is true?
Answer:
a
Step-by-step explanation:
solve for y in one equation
2x + y = -4
y = -4 - 2x
plug y into the other equation
5x + 3y = -6
5x + 3(-4 - 2x) = -6
5x -12 -6x = -6
-x - 12 = -6
-x = 6
x = -6
plug x into the equation to find y
y = -4 - 2x
y = -4 - 2(-6)
y = 8
ordered pair: (-6,8)
Which statement best describes g(x) = 3 x + 6 - 8 and the parent function f(x) = 3x ?
The domains of g(x) and f(x) are the same, but their ranges are not the same.
The ranges of g(x) and f(x) are the same, but their domains are not the same.
The ranges of g(x) and f(x) are the same, and their domains are also the same.
The domains of g(x) and f(x) are the not the same, and their ranges are also not the same.
Answer:
The answer is C: the ranges of g(x) and f(x) are the same, and their domains are also the same.
Step-by-step explanation:
Just took the test on edge!! :)
Option C The ranges of g(x) and f(x) are the same, and their domains are also the same is correct.
What is domain?
List of values of x an equation can satisfy is called Domain.
What is range?
List of values y the function can generate is called range
For example, f(x)=x
it can satisfy real domain i.e. x∈R
and range is R
g(x) = 3 x + 6 - 8 and f(x) = 3x
Domain for both the function is R
Both the function can satisfy all the real numbers, so its range is also R.
Therefore,Option C The ranges of g(x) and f(x) are the same, and their domains are also the same is correct.
Learn more about domain and range,
https://brainly.com/question/2264373
#SPJ2
Find the value of the ratio x ÷ y if the equation is 5x²-13xy+8y²
Answer:
x÷y=8/5 or 1÷1
Step-by-step explanation:
Please mark as brainliest
In the sketch below, two parallel lines are cut by a transversal.
Answer:
m<1 = 150°
Step-by-step explanation:
Given:
m<1 = (4x + 50)°
m<2 = (7x - 25)°
Required:
m<1
Solution:
To find m<1, we need to create an equation that will enable us determine the value of x.
Thus,
4x + 50 = 7x - 25 => corresponding angles are congruent to each other
4x + 50 - 7x = 7x - 25 - 7x (subtraction property of equality)
-3x + 50 = - 25
-3x + 50 - 50 = -25 - 50 (substraction property of equality)
-3x = -75
-3x/-3 = -75/-3 (division property of equality)
x = 25
✅m<1 = (4x + 50)°
Plug in the value of x
m<1 = 4*25 + 50 = 100 + 50
m<1 = 150°
If the critic rates a total of 100 movies, what is the best prediction for the number of movies she gives exactly 3 stars?
А
27
B
47
50
D
35
Answer:
I think its gonna be 35 I'm not sure
The height of one cylinder is 8 cm, and the radius of its base is 5 cm. The height of a second cylinder is 24 cm, and the radius of its base is 5 cm. How many times the volume of the first cylinder is the volume of the second cylinder?
Answer:
Step-by-step explanation:
volume₁ = π5²·8 = 200π cm³
volume₂ = π5²·24 = 600π cm³
volume₂ = 3×volume₁
Answer:
It is 3, hopefully you got a good score! :D
Step-by-step explanation:
What is the perimeter and area of the composite figure?
Step-by-step explanation:
▪AB = AC - EF
= 13 cm - 7 cm
= 6 cm
▪BD = CF - DE
= 16 - 8 cm
= 8 cm
BC = EF
perimeter = CF + EF + DE + AD + AB + BC
= 16 + 7 + 8 + 10 + 6 + 7
= 54 cm
Area of triangles = 1/2 × AB × BD
= 1/2 × 6 × 8
= 48/2
= 24 cm²
Area of rectangle = CF × EF
= 16 × 7
= 112 cm²
the total area = 24 + 112
= 136 cm²
#CMIIW
what is the value of x ?
a. 10.4
b. 52
c. 61.6
d. 92
A: 49
B: 33
C: 57
D: 16
Answer:
d
Step-by-step explanation:
i believe its 49 - 33= answer bc 49=49
Answer:
16°
Step-by-step explanation:
The two angles are vertical, meaning that they are the same
33 + 16 = 49
HELPPP I MAKE BRAINLIESTT
A seamstress charges a $5 fee per garment, plus $15 for each hour of work that the garment requires. The graph below shows the cost of having a single garment fixed by the seamstress, according to the number of hours of work that are needed.
Which linear function models the data?
A. c(t) = 5t
B. c(t) = 15t
C. c(t) = 5 + 15t
D. c(t) = 15 + 5t
Answer:
C. c(t) = 5 + 15t
Step-by-step explanation:
Well because the initial fee is $5, the answer must have the value of 5 without a variable next to it because this is the y-intercept.
(Only the slope will have the t next to it.)
Because $15 is charged EACH HOUR this would be the slope because there is a constant increase
Therefore c(t) = 5 + 15t
Answer:
C. c(t) = 5 + 15t
Step-by-step explanation:
She charges $15 per hour, so each hour (represented by "t") she earns 15 dollars. She also charges a $5 fee per germent. So she would get $5 plus 15 times however many hours she worked. So your answer would be c(t) = 5 + 15t.
what is -2 x 3 i do not understand this and this is my last problem
Answer:
-6
Step-by-step explanation:
if they were both positive numbers, it would be 6. But when you multiply a negative by a positive, the answer is negative.
Answer:
-6
Step-by-step explanation:
When you multiply a positive number by another positive number, you will always get a positive number as your answer. Same thing for negative. If you multiply a negative by a negative, you will always get a positive. However, when you multiply a negative by a positive, you will always get a negative number.
Since you know this, you can multiply 2 by 3, which is 6. Because 2 is negative and 3 is positive, you know that the answer must be negative. Therefore, you add the negative symbol to 6, giving you -6.
I hope this isn't too confusing. Please let me know if you have any more questions. Good luck!
Louis has a bag of 2510 shells each pen shell is 18 cm long what is the combine length of the pen shells in meters
Answer:
45180cm
Step-by-step explanation:
You have to multiply the amount of shells by the length on one shell to get the length of all of them combined so, 2510 multiplied by 18 is 45180.
Together, Dien and Jane can eat 2/3 of a pizza in 4 seconds. How long would it take each of them to eat the whole pizza alone if Jane can eat a pizza 5 seconds faster than Dien?
Answer:
Dien - 15 seconds, Jane - 10 secondsStep-by-step explanation:
Together:
2/3 of pizza ⇒ 4 secondsFull pizza ⇒ 4 ÷ 2/3 = 6 secondsDien needs x seconds to eat pizza
Jane needs x - 5 seconds to eat pizza
In one second, Dien can eat 1/x, Jane can eat 1/(x - 5), together 1/6 of a pizza
1/x + 1/(x - 5) = 1/6x(x - 5) = 6(x + x - 5)x² - 5x - 12x + 30 = 0x² - 17x + 30 = 0(x - 15)(x - 2) = 0x = 15 (x = 2 is discounted as not realistic)Dien can eat a pizza in 15 seconds, Jane can eat a pizza in 10 seconds