Complete question is;
Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 13. Use the empirical rule to determine the following.
(a) What percentage of people has an IQ score between 87 and 113?
(b) What percentage of people has an IQ score less than 74 or greater than 126?
(c) What percentage of people has an IQ score greater than 139?
Answer:
A) 68% of the people had an IQ score between 87 and 113
B) 5% of the people had IQ scores less than 74 and greater than 126.
C) 0.15% had an IQ score greater than 139
Step-by-step explanation:
We are given;
Mean; x¯ = 100
Standard deviation; σ = 13
According to the empirical rule in statistics;
>> 68% of the data lies within one standard deviation of the mean
>> 95% of the data lies within two standard deviations of the mean
>> 99.7% of the data lies within three standard deviations
A) We want to find the percentage of people with an IQ score between 87 and 113.
Within one standard deviation, we have;
x¯ ± σ
>> (100 - 13), (100 + 13)
>> (87, 113) which is the range we are looking for.
Thus, 68% of the people had an IQ score between 87 and 113
B) we want to find percentage of people has an IQ score less than 74 or greater than 126.
Let's first find those who had between 74 and 126.
Let's use two standard deviations within the mean.
x¯ ± 2σ
>> (100 - (2×13)), (100 + (2×13))
>> (74, 126) which is the range we are looking for.
So percentage that have IQ scores between 74 and 126 is 95%
Thus;
Percentage of those who had less than 74 and greater than 126 is;
P = 1 - 95%
P = 5%
C) we want to find the percentage of people that had an IQ score greater than 139.
Let's use the z-score formula;
z = (x¯ - μ)/σ
z = (139 - 100)/13
z = 39/13
z = 3
This means it is 3 standard deviations above the mean.
Thus;
Since it's one side outside the mean, then;
Percentage of people with an IQ score greater than 139 = (1 - 99.7%)/2 = 0.3%/2 = 0.15%
On a piece of paper, graph y< 2x+2. Then determine which answer choice
matches the graph you drew.
А
B
С
D
(0,2)
(0.2
(0.2)
(0,2)
1.4.1)
1.4.1
(1.4.1)
(4-1)
A. Graph A.
B. Graph B
ОО O
C. Graph C
D. Graph D
Answer:
graph A
Step-by-step explanation:
because 2x+2,x ...-1
so it is lies in graph A
27.4 is 2.5% of what number
Answer:
1096
Step-by-step explanation:
0.025x = 27.4
x = 1096
Find the slope of the line that passes through (1, -19) and (-2, -7)
Answer:
y = -4x-15
Step-by-step explanation:
y = ax+b
-19=a+b
-7=-2a+b
==> a = -4
b = -15
A news article estimated that only 4% of those age 65 and older who prefer to watch the news, rather than to read or listen, watch the news online. This estimate was based on a survey of a large sample of adult Americans. Consider the population consisting of all adult Americans age 65 and older who prefer to watch the news, and suppose that for this population the actual proportion who prefer to watch online is 0.04. (a) A random sample of n = 100 people will be selected from this population and p, the proportion of people who prefer to watch online, will be calculated. What are the mean and standard deviation of the sampling distribution of p? (Round your standard deviation to four decimal places.) mean 0.04 standard deviation 0.0196 (b) Is the sampling distribution of p approximately normal for random samples of size n = 100? Explain. The sampling distribution of p is approximately normal because np is less than 10. O The sampling distribution of p is approximately normal because np is at least 10. The sampling distribution of p is not approximately normal because np is less than 10. The sampling distribution of p is not approximately normal because np is at least 10. The sampling distribution of is not approximately normal because n(1-P) is less than 10. (c) Suppose that the sample size is n = 400 rather than n = 100. What are the values for the mean and standard deviation when n = 400? (Round your standard deviation to four decimal places.) mean 0.03 standard deviation 0.0085 Does the change in sample size affect the mean and standard deviation of the sampling distribution of ? If not, explain why not. (Select all that apply.) 2 When the sample size increases, the mean increases. When the sample size increases, the mean decreases. When the sample size increases, the mean stays the same. The sampling distribution is always centered at the population mean, regardless of sample size. When the sample size increases, the standard deviation increases. When the sample size increases, the standard deviation decreases When the sample size increase the standard deviation stays the same. The standard deviation of the sampling distribution is always the same as the standard deviation of the population distribution regardless of sample size. Suppose that the sample size is n = 400 rather than n = 100. What are the values for the mean and standard deviation when n = 400? (Round your standard deviation to four decimal places.) mean 0.03 standard deviation 0.0085 Does the change in sample size affect the mean and standard deviation of the sampling distribution of p? If not, explain why not. (Select all that apply.) When the sample size increases, the mean increases. When the sample size increases, the mean decreases. When the sample size increases, the mean stays the same. The sampling distribution is always centered at the population mean, regardless of sample size. When the sample size increases, the standard deviation increases. When the sample size increases, the standard deviation decreases. When the sample size increases, the standard deviation stays the same. The standard deviation of the sampling distribution is always the same as the standard deviation of the population distribution, regardless of sample size. (d) is the sampling distribution of p approximately normal for random samples of size n = 400? Explain. The sampling distribution of p is approximately normal because np and n(1 - p) are both at least 10. The sampling distribution of p is approximately normal because np and n(1 - 0) are both less than 10. The sampling distribution of p is not approximately normal because np and n(i - p) are both at least 10. • The sampling distribution of p is not approximately normal because np and n(1-P) are both less than 10. The sampling distribution of p is not approximately normal because only np is at least 10.
Answer:
(a) The mean is 0.04
The standard deviation is approximately 0.0196
(b) The sampling distribution of p is not approximately normal because n·p is less than 10
(c) Given that n = 400, we have;
i) The mean is 0.04
The standard deviation is approximately 0.0098
ii) The sampling distribution is always centered at the population mean, regardless of the sample size
iii) When the sample size increases, the standard deviation decreases
(d) The sampling distribution of p is approximately normal because n·p and n·(1 - p) are both at least 10
Step-by-step explanation:
(a) From the question, we have that the actual proportion of all adult Americans who watch online = 0.04
Given that the sample size, 'n' is 100 which is larger than 30, we can assume that the distribution of the sample mean is normal
Therefore, the mean (proportion) of the sample, P = The mean (proportion) of the population = 0.04
The mean, P = 0.04
The standard deviation, σ = √((p·(1 - p))/n)
∴ σ = √((0.04·(1 - 0.04))/100) ≈ 0.0196
(b) The sampling of p is approximately normal, given that the sample size, 'n' = 100 which is randomly selected from the population, we have;
The sampling distribution = n·p = 100 × 0.04 = 4 <10
Therefore, the sample is not approximately normal because the sampling distribution, n·p = 4 which is less than 10
c) Given that n = 400, we have;
p = 0.04 = The [population mean
The standard deviation, σ √((0.04·(1 - 0.04))/400) ≈ 0.0098
According to the central limit theorem when the sample size increases, the mean approaches the population mean, therefore, the sampling distribution is always centered at the population mean, regardless of the sample size
When the sample size increases, the standard deviation decreases
(d) Given that when the sample size, n = 400, we have;
n·p = 400 × 0.04 = 16 > 10
Similarly, we have;
n·(1 - p) = 400 × (1 - 0.04) = 384 > 10
The sample is approximately normal
Therefore, the sampling distribution of p is approximately normal because np and n(1 - p) are both at least 10
Easy question What is the answer??
Answer:
72.5
Step-by-step explanation:
Answer:
72.5
Step-by-step explanation:
The graph shows two lines, A and B. How many solutions are there for a pair of equations for lines A and B? Explain your answer. If I get it right I’ll give brainliest!!!
Answer:
There is only 1 solution
[tex](x,y) = (1,4)[/tex]
Step-by-step explanation:
Given
Lines A and B
Required
The number of solution for a pair of A and B
From the graph, lines A and B have only one point of intersection.
This point of intersection represents the solution
Since, there is only 1 point, there is only one solution.
And the solution is:
[tex](x,y) = (1,4)[/tex]
A survey was conducted to determine how many movies were seen in one month among the 26 students in Mrs. Hampton’s sixth-grade class. The results are shown in the dot plot below.
a) Calculate the measures of center for the data in the dot plot, rounding your answers to the nearest tenths place. Show how you determined your answer. (2 points)
Answer:
in the question,there is no dot plot
Martin and Clara decide to keep track of the number of different colors in two brands of tennis shoes, brand A and brand B. Their results are represented by the dot plots. The mean absolute deviation for brand A is . The mean absolute deviation for brand B is . The mean absolute deviations for the two brands similar.
The following conclusion is reached concerning the results represented by the dot plots:
The Mean Absolute Deviation for brand A is: 2.02 The Mean Absolute Deviation for brand A is: 1.905 The Mean Absolute Deviation for the two brands ARE similar.What is the Mean Absolute Deviation?The mean absolute deviation is a test of variability of a data set which is the average distance between each of the data point in the data set and the mean.
Find the mean absolute deviation for each dot plots.
Mean Absolute Deviation for Brand A:
The points are, 1,1,2,2,2,3,4,4,5,5,5,5,6,6,7,7,8,8,8,9
Mean = (1 + 1 + 2 + 2 + 2 + 3 + 4 + 4 + 5 + 5 + 5 + 5 + 6 + 6 + 7 + 7 + 8 + 8 + 8 + 9)/20 = 98/20
Mean = 4.9
Mean Absolute Deviation = [(1 - 4.9) + (1 - 4.9) + (2 - 4.9) + (2 - 4.9) + (2 - 4.9) + (3 - 4.9) + (4 - 4.9) + (4 - 4.9) + (5 - 4.9) + (5 - 4.9) + (5 - 4.9) + (5 - 4.9) + (6 - 4.9) + (6 - 4.9) + (7 - 4.9) + (7 - 4.9) + (8 - 4.9) + (8 - 4.9) + (8 - 4.9) + (9 - 4.9)] / 20
= [(3.9) + (3.9) + (2.9) + (2.9) + (2.9) + (1.9) + (0.9) + (0.9) + (0.1) + (0.1) + (0.1) + (0.1) + (1.1) + (1.1) + (2.1) + (2.1) + (3.1) + (3.1) + (3.1) + (4.1)] / 20
= 40.4/20
Mean Absolute Deviation for brand A = 2.02
Mean Absolute Deviation for Brand B:
The points are, 1,3,3,4,4,4,4,4,5,5,5,6,6,6,6,8,8,9,10,10
Mean = (1 + 3 + 3 + 4 + 4 + 4 + 4 + 4 + 5 + 5 + 5 + 6 + 6 + 6 + 6 + 8 + 8 + 9 + 10 + 10)/20
Mean = 111/20 = 5.55
Mean Absolute Deviation = [(1 - 5.55) + (3 - 5.55) + (3 - 5.55) + (4 - 5.55) + (4 - 5.55) + (4 - 5.55) + (4 - 5.55) + (4 - 5.55) + (5 - 5.55) + (5 - 5.55) + (5 - 5.55) + (6 - 5.55) + (6 - 5.55) + (6 - 5.55) + (6 - 5.55) + (8 - 5.55) + (8 - 5.55) + (9 - 5.55) + (10 - 5.55) + (10 - 5.55)] / 20
Mean Absolute Deviation = 38.1/20
Mean Absolute Deviation for brand B = 1.905
Therefore, the following conclusion is reached concerning the results represented by the dot plots:
The Mean Absolute Deviation for brand A is: 2.02 The Mean Absolute Deviation for brand A is: 1.905 The Mean Absolute Deviation for the two brands ARE similar.Learn more about mean absolute deviation on:
https://brainly.com/question/17381861
x/4−1=3
What is the value of x?
Answer:
x = 16
Step-by-step explanation:
x/4 - 1 = 3
x/4 = 3+1
x/4 = 4
x = 4*4
x = 16
Answer:
x=16
Step-by-step explanation:
always multiply denominator by whatever it is to the number behind the equl sign after subtracting that one it would be whatever that number is *4
It’s worth 13 points thank you!
:)
Answer: the answer is the 3rd bubble:)
Step-by-step explanation:
Click an Item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the
correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag
the item to the trashcan. Click the trashcan to clear all your answers.
Express In simplified exponential notation.
18a^3b^2/ 2ab
Answer:
18a^3b^2/2ab
To simplify the given expression, we apply property of exponents
18/2 = 9
x^m / x^n= x^ (m-n) In division we subtract the exponents
So given expression becomes
9a^2b
The answer has only positive exponents
i think this is what you want?
The simplified exponential notation of the given expression is [tex]9a^2b[/tex].
The given expression is: [tex]\frac{18a^3b^2}{2ab}[/tex]
What is an exponential expression?An expression in the form of [tex]a^pb^qc^r[/tex].. is called exponential expression.
We can write the above expression as:
[tex](\frac{18}{2} )(\frac{a^{3} }{a} )(\frac{b^{2} }{b} )[/tex]
We know that [tex]\frac{a^m}{a^n} =a^{m-n}[/tex]
[tex]\frac{a^{3} }{a} =a^{3-1} =a^{2} \\\frac{b^{2} }{b}=b^{2-1} =b[/tex]
So, [tex](\frac{18}{2} )(\frac{a^{3} }{a} )(\frac{b^{2} }{b} )[/tex] =[tex]9a^2b[/tex]
Hence, the simplified exponential notation of the given expression is [tex]9a^2b[/tex].
To get more about polynomials visit:
https://brainly.com/question/2833285
simplify 3 - 5 (-3n + 5)
Answer:
I think it's 15n-22
Step-by-step explanation:
I hope this is correct!
12y2/3, 14a^3a ,b^5c a monomial or not
Answer:
The fist one doesnt make sense as a term but other two are monomials
Step-by-step explanation:
simplist form for 15/25
Answer:
15/25 = 3/5
Step-by-step explanation:
The simplest form of 1525 is 35.
have a good day
may i please have a brianlliest
thank you
Answer: 3/5
Explanation: Dividing both 15 and 25 by 5 gives you 3 and 5; 3/5.
The perimeter of a square is given as 12x plus 20 write two different expressions to represent its perimeter for one way factors the expression using the gcf
Favorite Book Types
What is the missing value of the circle graph? *
(10 Points)
3%
Romance
x х
Comedy
16%
Fantasy
14%
Science
Fiction
18%
Mystery
10%
Historical
Fiction
61%
O 39%
12%
O 15%
Answer:
39
Step-by-step explanation:
10+18+14+16+3=61
100-61=39
The graph shows a proportional relationship. Which equation matches the graph?
Answer:
3x
Step-by-step explanation:
(7^3)^3
Simplify.
Rewrite the expression in the form 7^n
Step-by-step explanation:
✧ [tex] \underline{ \underline{ \large{ \tt{R\: E \: M \: E \: M \: B \: E \: R}}} }: [/tex]
If [tex]( {x}^{a} )^{b} [/tex] is an algebraic term then [tex] {(x}^{a} )^{b} = {x}^{a \times b} [/tex] i.e When an algebraic term in the index form is raised to another index , the base is raised to the product of two indices.
⟶ [tex] \large{ \tt{( {7}^{3} ) ^{3} = {7}^{3 \times 3} = {7}^{9}}} [/tex]
☥ [tex] \boxed{ \boxed{ \large \tt{Our \: Final \: Answer : \underline{ \tt{ {7}^{9}}}}}} [/tex]
Hope I helped ! ♡
⋆ Have a wonderful day / night ! ♪
Let me know if you have any questions regarding my answer! ツ
[tex] \underline{ \underline{ \mathfrak{Carry \: On \: Learning}}}[/tex] !! ✎
▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁
f(x) = -2x^2-4x+11
in the standard form
f(x) = a(x – h)^2+k
Step-by-step explanation:
f(x) = -2x^2-4x+11
y = -2(x+1)²+13
Use the vertex form, y=a(x−h)²+k, to determine the values of a, h, and k.
a= -2
h= 1
k= 13
Final answer is, f(x) = -2(x - 1)² + 13
Answer:
f(x) = - 2(x + 1)² + 13
Step-by-step explanation:
f(x) = - 2x² - 4x + 11
f(x) = a(x - h)² + k
a = - 2, b = - 4, c = 11
h = - [tex]\frac{b}{2a}[/tex]
h = - [tex]\frac{-4}{2(-2)}[/tex] = - 1
k = - 2( - 1)² - 4( - 1) + 11 = 13
f(x) = - 2(x + 1)² + 13
Chace scored 7, 9, 5, 3, 15 and 15 points in 6 basketball games. What is the mode of the number of points he scored in those games?
Answer:
15
Step-by-step explanation:
mode is the number that appears most often. 7,9,5 and 3 all show up once, but 15 shows up twitch
PLEASE ANSWER!!!!!!!!!!!!!!!!!!!!!!!!
I am pretty sure the answer is letter C
I got 10 but can someone make sure because I want to get a 100
Answer:
i think 10
Step-by-step explanation:
DO WHATEVER YOU CAN TO HELP ME
Answer:A,C,D
Step-by-step explanation:
Answer:
A, C, D
Step-by-step explanation:
4-1=3 (correct)1+4=6 (incorrect)3x4=12 (correct)20÷5=4 (correct)3-4=1 (incorrect)Which is the equation for the line that has a slope of 12 and passes through the point (3, 20)?
Answer:
y=12x-16
Step-by-step explanation:
y-y1=m(x-x1)
y-20=12(x-3)
y=12x-36+20
y=12x-16
Which statement describes the solution to this system of equations?
2x – 4y = 8
8x - 16y = 32
А
There is exactly one solution, (2,4)
B
There is exactly one solution, (8,32)
ОООО
с
There is no solution to the system of equations
D
There is an infinite number of solutions to the system of equations.
9514 1404 393
Answer:
D There is an infinite number of solutions to the system of equations
Step-by-step explanation:
When you put the first equation in standard form by dividing it by 2, you get ...
x -2y = 4
When you put the second equation in standard form by dividing it by 8, you get ...
x -2y = 4
These are the same equation, so describe the same line. There are an infinite number of (x, y) pairs that will satisfy this equation.
There is an infinite number of solutions.
paul invested $400 into an account with a 5.5% interest rate compounded monthly. How much will paul's investment be worth in 8 years?
Answer:
3024
Step-by-step explanation:
get the answer of 5.5% of 400, which is 22.
subtract 22 from 400, which is 378.
multiply 378 by 8, which is 3024.
Answer:
By using a compound interest calculator, we can know the answer which is $621
Step-by-step explanation:
10 exponent 2 + (6-3) + ( 4x9) =
Answer:
10 exponent 2 + (6-3) + (4x9) = 139
Step-by-step explanation:
A circle has a diameter of 24 cm. Which expression
could represent the area of this circle in square cm?
how many cookies will Tina have if she bakes 7 more batches more than the maximum number of batches in the table
Cookies baked (y) is a function of number of batches (x).
Number of batches___total number of cookies
5__180
6__198
7__216
8__234
9__252
Answer:
5
Step-by-step explanation:
Find the area of the rectangle 2 1/4 1 1/2
Answer:
3 3/8
I converted the fractions in to decimals, multiplied them and then converted the decimal into a fraction.