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%
The normal distribution is:
A. a distribution that can be modeled by a bell-shaped curve, with the
mean, median, and mode all the same value and the proportion for
any range of values defined in a table of normal curve areas (or
probabilities)
B. a bell-shaped density curve defined by the population mean (4),
which determines the position of the center of the curve, and the
population standard deviation (c), which determines the height
and spread of the curve.
C. any distribution that can be modeled by a density curve.
D. a set of values that lie directly on a plot of a bell-shaped density
curve, which is defined by the population mean (x) and the
population standard deviation ().
E. an imaginary histogram in which the width of each class is zero,
and the number of population members is infinite.
The lengths of the three sides of a triangle are
x cm, 2x cm and 3x cm. Its perimeter is 30 cm.
Evaluate x.
Answer:
Answer is 5
Step-by-step explanation:
x+2x+3x=30
6x=30
x=5
Use the information to answer the following questions.
Jocelyn and Kari’s math quiz scores are shown.
Jocelyn: 86, 87, 95, 72, 78, 80
Kari: 88, 78, 93, 81, 75, 92
Activity 1 of 2
Part A: Based on the samples, which student generally has higher quiz scores?
A.
Kari, because the mean and median of her scores is 84.5.
B.
Kari, because the range of her scores is 18.
C.
Jocelyn, because the interquartile range of her scores is 9.
D.
Jocelyn, because she had a maximum score of 95.
Activity 2 of 2
Part B: Suppose both girls got a 90% on their next math quiz. Which student will see a greater increase in her overall math grade?
A.
Jocelyn, because her grade will increase by 1 point.
B.
Kari, because her grade will increase by 0.8 points.
C.
Kari, because her grade will increase to 85.3.
D.
Jocelyn, because her grade will increase to 84.
Answer:
A
Step-by-step explanation:
Part A, A. Kari, because the mean and median of her scores is, 84.5.
Part B, Jocely will see a greater increase overall as her previous average is less.
What are mean, median, and mode?The three main methods for identifying the average value of a set of integers are mean, median, and mode.
Adding the numbers together and dividing the result by the total number of numbers in the list yields the arithmetic mean.
The middle value in a list that is arranged from smallest to greatest is called the median.
The value that appears the most frequently on the list is the mode.
From the given information, The average score of Jocelyn is,
= (86 + 87 + 95 + 72 + 78 + 80)/6.
= 83.
And Similarly, The average score Kari is,
= (88 + 78 + 93 + 81 + 75 + 91)/6.
= 84.5.
Therefore, Kari scores better overall.
If they both get 90% on their next math quiz Jocely will see a greater increase overall as her previous average is less.
learn more about mean here :
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If Sally walks 2 meter it takes her 1 second. If she walks 4 meters it takes her 2 seconds and 6 meters takes her 3 seconds. Is this a linear situation? Make a table and plot the points in the table to determine whether the following relationship is linear If it is, write an equation that represents the data.
Answer:
y=2x
Step-by-step explanation:
2 1
4 2
6 3
QUICK I NEED THIS ANSWER QUICKLY
Can someone help fast to find a and c
Answer: 15 10
Step-by-step explanation:
Does anyone know how to do this
csc x ( sin x + cos x) = 1 + cot x
9514 1404 393
Explanation:
Use the identities ...
csc(x) = 1/sin(x)
cot(x) = cos(x)/sin(x)
__
[tex]\csc(x)(\sin(x)+\cos(x))=1+\cot(x)\\\\\dfrac{1}{\sin(x)}(\sin(x)+\cos(x))=1+\cot(x)\\\\\dfrac{\sin(x)}{\sin(x)}+\dfrac{\cos(x)}{\sin(x)}=1+\cot(x)\\\\1+\cot(x)=1+\cot(x)[/tex]
Please and I’ll give Brain list to you
Answer:
e
Step-by-step explanation:
e
Answer:
6
Step-by-step explanation:
PLEASE HELP ME ANYONE ???????????!!!
Answer:
A x>9
Step-by-step explanation:
add 4 to both sides and ta da
Answer:
x>9
Step-by-step explanation:
you move the negative 4 to the other side to get it away from x so then you can find the answer.
Hope this helps:)
PLEASE WILL MARK BRAINIEST!!!!!! Jameson and Quincy each deposit $7,000 into accounts that earn 6% interest, but Jameson earns annual simple interest while Quincy earns annual compound interest. Assuming neither one of them makes any deposits or withdrawals for 5 years, which of the following is a true statement?
Jameson will have about $9,367.58 less in his account than Quincy.
Jameson will have about $267.58 less in his account than Quincy.
Jameson will have about $2,367.58 more in his account than Quincy.
Jameson will have about $2,100 more in his account than Quincy.
Jameson will have about $267.58 less in his account than Quincy.
What is Compound Interest?Compound interest is the interest calculated on the principal and the interest accumulated over the previous period.
Here, Jameson deposit Principal = $ 7000
Duration = 5 years
Rate of interest = 6 % SI per annum.
For simple Interest, Amount = P(1+RT)
Total amount in Jameson at the end of 5 years = 7000 ( 1 + 0.06 X 5)
= 7000 X 1.3
= $ 9100
Quincy deposit Principal = $ 7000
Duration = 5 years
Rate of interest = 6 % CI per annum.
For Compound Interest, Amount = P(1+R)ⁿ
Total amount in Quincy at the end of 5 years = 7000 ( 1 + 0.06)⁵
= 7000 X 1.34
= $ 9367.58
Thus, Jameson will have about $267.58 less in his account than Quincy.
Learn more about Compound Interest from:
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Which graph represents the solution set for the inequality: y > x-1
Answer:
F
Step-by-step explanation:
Liliana used 4 dark power crystals to raise 14 zombie soldiers. She wants to know how many zombie soldiers (z) left parenthesis, z, right parenthesis she can raise with 10 dark power crystals.
Answer:
So.. Liliana used 4 crystals to race 14 zombie soldiers.
14 / 4 = 3.5. She can race 3.5 zombie soldiers if she uses 1 crystal. So, all you need to do it multiply 3.5 by 10 and you end up with 35.
So, Liliana is able to race 35 zombie soldiers with 10 power crystals.
Glad I could help!
Step-by-step explanation:
Maya has 120 caramel apples to sell. Each caramel apple is covered with one topping. •
• 1/5of the caramel apples are covered with peanuts.
• 1/3are covered with chocolate chips
• 3/10 are covered with coconut.
• The rest are covered with sprinkles.
How many caramel apples are covered with sprinkles?
A 100
B 33
C 25
D 20
Step-by-step explanation: D. 20
Brainiest guranted question below.
Answer:
48
Step-by-step explanation:
30 is 5/8 of ?
30x8=240
240/5=48
(18 Math teachers and 30 non-Math teachers)
Can someone help me ?
Answer:
The second one doesn't match.
A+5 expressed as a difference
Answer:
A-(-5) = A+5
it is the answer
Answer:
a-(-5)
Step-by-step explanation:
Since it's originally an addition question but you want to write it as a difference (subtraction) question, you would use double negative signs. Whenever there are two double negatives next to each other, it counteracts and becomes a positive sign, however you still wrote it as a subtraction question.
Hope this helps
Solve (x - 4)2 = 5.
help
Answer:
13/2
Step-by-step explanation:
2x-8=5
2x=5+8
2x=13
x=13/2
hope it helps
[tex] \binom{ \sin( \alpha) + \sin( 2alpha ) }{1 + \cos( \alpha ) + \cos(2 \alpha ) } = \tan( \alpha ) [/tex]
I see you use the TeX command "\binom" for binomial coefficient, but I think you meant to use "\frac" to write a fraction, namely,
[tex]\dfrac{\sin(\alpha)+\sin(2\alpha)}{1+\cos(\alpha)+\cos(2\alpha)}=\tan(\alpha)[/tex]
and I assume you're supposed to establish an identity.
Recall the double angle identities for cos and sin :
cos(2α) = cos²(α) - sin²(α) = 2 cos²(α) - 1
sin(2α) = 2 sin(α) cos(α)
Now expand the left side as
(sin(α) + sin(2α)) / (1 + cos(α) + cos(2α)) = (sin(α) + 2 sin(α) cos(α)) / (1 + cos(α) + 2 cos²(α) - 1)
Factor sin(α) from the numerator, and after canceling the 1s in the denominator and factor cos(α) :
… = [sin(α) (1 + 2 cos(α))] / [cos(α) (1 + 2 cos(α))]
Cancel the factors of 1 + 2 cos(α) :
… = sin(α) / cos(α)
which is equivalent to
… = tan(α)
by definition of tan.
The sales tax rate is 8.5%. If Helen buys a pillow priced at $18, how much tax will she pay?
Answer:
$1.53 for tax
Step-by-step explanation:
18 times .085 = 1.53
Consider the graphs of f(x) and g(x).
ent
f(x)
g(x)
If g(x) = f(x) + k, find the value of k.
Answer:
K=7
Step-by-step explanation:
hope it helps you
have a wonderful day!!!
55 is 22% of what number?
Answer:
250
Step-by-step explanation:
100 / 22 = 4.54545455
4.54545455 x 55 = 250
Answer: 250
Step-by-step explanation:
Ur welcome
(55x100)/22
NO LINKS PLEASE and make sure its correct
Answer:
x= -7
Step-by-step explanation:
Answer:
LCM=4
4x3 /4 x 3/4 (x+21)=101/2x4
multiply through by the lcm
3x=20-21
3x/3=-1/3
the answer is-1/3
hope it helps
PLease help me asnwer this!!
Answer:
The answer is 60x500=30000
Step-by-step explanation:
30000 is your answer
Which equation would we use to figure out this problem? Rachael
started off with $400 in her savings account in 2005. It earns 3% interest
each year. She wants to know how much money she'll have in the account
in 2022.
Answer:
She'll have $661 in the account in 2022.
Step-by-step explanation:
Compound interest:
The amount of money earned in compound interest after t years is given by the following equation:
[tex]A(t) = A(0)(1+r)^t[/tex]
In which A(0) is the initial amount and r is the interest rate, as a decimal.
Rachael started off with $400. It earns 3% interest each year.
This means that [tex]A(0) = 400, r = 0.03[/tex]
So
[tex]A(t) = A(0)(1+r)^t[/tex]
[tex]A(t) = 400(1+0.03)^t[/tex]
[tex]A(t) = 400(1.03)^t[/tex]
She wants to know how much money she'll have in the account in 2022.
17 years after 2005, which means that this is A(17). So
[tex]A(17) = 400(1.03)^{17} = 661[/tex]
She'll have $661 in the account in 2022.
A baseball player throws a ball from second base to home plate. How far does the player throw the ball? Include a diagram showing how you got your answer. Decide how many decimal points of accuracy are reasonable. Explain your reasoning.
Answer:
127 ft 3 3/8in
Step-by-step explanation:
Assuming the field is regulation (I can't see the model), the answer is 127 feet and 3 3/8 inches.
5/6 minus (- 3/4)
HELP PLS
Answer:
In order to solve this problem, you have to find the lowest common denominator. Take multiples of both 6 and 4 and see which is the lowest you have in common.
4: 4, 8, 12, 16, 20
6: 6, 12, 18, 24
So 12 is the lowest common multiple....
5/6 x ?/? = ?/12 (you have to multiply the numerator and the denominator by the same number)
3/4 x ?/? = ?/12 (you have to multiply the numerator and the denominator by the same number)
When the denominators are the same, you can subtract the numerators. The denominator will stay 12!
Step-by-step explanation:
YAY! I want a brain
Answer:
Exact Form: 19/12
Decimal form:1.583
Mixed number form: 1 7/12
Step-by-step explanation:
hope i was right!
Determine if the triangle are similarity side-side-side similarity
The height of a building is 60 m long to the nearest degree what is the angle of elevation of the sun on a building cast a shadow that is 80 m long
Answer:
80m
Step-by-step explanation:
Find the inequality represented by the graph
Answer: y<x-1
Step-by-step explanation:
So first we have to find the blue line. y=mx+b is the equation. For slope it is 0--1 which is 1 and 1-0 which is 1 so the slope is just one or x now we need to find the y intercept which is just -1. So y<(is less than)x-1! Hope this helps :)
please help im literally crying im desperate i can't fail please
Answer:
as my caculation the answer is : 11.3137 m3
Step-by-step explanation:
i use my caculator