Using the normal distribution, it is found that:
a) The 65th percentile is of 37.31.
b) The 90th percentile is of 42.68.
c) There is a 0.5705 = 57.05% probability of getting a raw score between 28 and 38.
d) There is a 0.0919 = 9.19% probability of getting a raw score between 41 and 44.
In 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.In this problem:
The mean is of 35, hence [tex]\mu = 35[/tex]The standard deviation is of 6, hence [tex]\sigma = 6[/tex]Question a:
The 65th percentile is X when Z has a p-value of 0.65, so X when Z = 0.385.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.385 = \frac{X - 35}{6}[/tex]
[tex]X - 35 = 0.385(6)[/tex]
[tex]X = 37.31[/tex]
The 65th percentile is of 37.31.
Question b:
The 90th percentile is X when Z has a p-value of 0.9, so X when Z = 1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{X - 35}{6}[/tex]
[tex]X - 35 = 1.28(6)[/tex]
[tex]X = 42.68[/tex]
The 90th percentile is of 42.68.
Question c:
The probability is the p-value of Z when X = 38 subtracted by the p-value of Z when X = 28, hence:
X = 38:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{38 - 35}{6}[/tex]
[tex]Z = 0.5[/tex]
[tex]Z = 0.5[/tex] has a p-value of 0.6915.
X = 28:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{28 - 35}{6}[/tex]
[tex]Z = -1.17[/tex]
[tex]Z = -1.17[/tex] has a p-value of 0.121.
0.6915 - 0.121 = 0.5705.
There is a 0.5705 = 57.05% probability of getting a raw score between 28 and 38.
Question d:
The probability is the p-value of Z when X = 44 subtracted by the p-value of Z when X = 41, hence:
X = 44:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{44 - 35}{6}[/tex]
[tex]Z = 1.5[/tex]
[tex]Z = 1.5[/tex] has a p-value of 0.9332.
X = 41:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{41 - 35}{6}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a p-value of 0.8413.
0.9332 - 0.8413 = 0.0919
There is a 0.0919 = 9.19% probability of getting a raw score between 41 and 44.
A similar problem is given at https://brainly.com/question/24663213
The temperature of a substance in an experiment changes by 8.7F from 10 am to 1p.m. At 5p.m., the temperature is 33.5°F. It
is 2/3 of what the temperature was at 1p.m.
What was the temperature at 10 a.m. of the substance?
Enter your answer as a decimal in the box
Answer:
138
Step-by-step explanation:
the locus of all points that are the same distance from (3,-2) and (3,4) is one straight line. Draw this straight line
Answer:
No answer i can provide
Step-by-step explanation:
If you need to make a line on a graph, you need to plot at least 2 points. Luckily, the two points have been given.
Plot the points on your graph. for your first coordinate, go 3 over and down 2. for your second point, go over 3 and up by 4. for the line, draw it through your 2 points.
Hope this helps!
Answer:
line is y = 1
Step-by-step explanation:
the question is talking about loci, in this case 2 point
these 2 points are (3,-2) and (3,4)
draw a line to connect these to points and bisect the line.
to do this use a compass : put the compass more than half way and place it one the first point - draw an arc .
then draw another arc at the sencond point
were the 2 arcs meet draw a line - this straight line will be the answer.
y = 1
someone please help me
Answer:
FOURTH ONE DOWN
Step-by-step explanation:
Basically the the format is (vertical / horizontal), so CB and AD are both gonna be denominators (the bottom of the fraction).
** also next time please take a better picture i had to squint my eyes so hard **
Carlos bought 17 boxes of cereal. This is 20% of the total boxes at the store. In order to find the total number of boxes at the store, what do you need to find?
A) the part
B) the whole
C) the percent
D) benchmark percent
Answer:
The whole
Step-by-step explanation:
If the part is 20% then you already have a part of a whole, now you need to find the entire thing
can someone please help
E, C, F are the answers.
Hurry please
Answer ASAP
x-8/2=-14
solve for x
Answer:
-20
Step-by-step explanation:
-14 x 2 = -28
-28 + 8 = -20
There you go :D
Answer:
-10
Step-by-step explanation:
first Solve for the fraction
-8/2= -4
x-4= -14
next add the negative 4 to 14
x=-10
and there's you're answer!
2^-3 x 3^-2
what’s the answer?
Answer:
1/72Step-by-step explanation:
[tex]2^{-3} * 3^{-2} =[/tex][tex]1/2^3 * 1/3^2 =[/tex][tex]1/8*1/9=[/tex][tex]1/72[/tex][tex]\\ \sf\longmapsto 2^{-3}\times 3^{-2}[/tex]
[tex]\\ \sf\longmapsto( \dfrac{1}{2})^3\times( \dfrac{1}{3})^2[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{8}\times \dfrac{1}{9}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{72}[/tex]
I just woke up i need help ;-;
Answer:
i think that the correct answer is 7/12
Naomi’s recipe for baked beans calls for 715 cup of kidney beans. Each can of kidney beans holds 145 cups. How many cans of kidney beans will Naomi use to make the recipe?
Answer:
5 Cans
Step-by-step explanation:
Hoped this helped.
After working for 6 hours kevin earned 51.00. what is kevin's unti rate
Answer:
Kevin's unit rate is 8.5. This means Kevin earns $8.5 ever hour.
Step-by-step explanation:
51.00/6.
Hope this helps! :)
Answer:
He earns 8.5 every hour.
Step-by-step explanation:
You would have to find how much he earns every hour
6:51, divide 6 on both sides
1:8.5, earns 8.5 every 1 hour.
Translate the phrase into an algebraic expression.
The product of 6 and c
Answer:
c x 6 = x
Product judy basically means multiplication.
Translate sum of 4 and the quotient of n and 9
Step-by-step explanation:
The quotient of n and 9:
n / 9Sum of 4 and the quotient:
4 + (n/9)Does anyone know which one it is??
Answer:
Limited economic options
Step-by-step explanation:
Answer:
A i think
Step-by-step explanation:
do to the way peasants lived they did not have options most of the time
Which of the following is NOT a perfect square trinomial?
Group of answer choices
^2+20−100
4^2−20+25
^2+18+81
16^2−24+9^2
Answer:
x^2+20−100 and 16^2−24+9^2
Step-by-step explanation:
Show that x^2-8x+20 can be written in the form (x-a)^2+a where a is an integer
Step-by-step explanation:
Let's complete the square
x²-8x=-20
x²-8x+(-4)²=-20+(-4)²
x²+(-4)²=-20+16
(x-4)²=-4
(x-4)²+4
where a is an integer as required
What is the remainder when the polynomial 8x2 4x−3 is divided by 2x−1?.
Answer:
Did the quiz :)
Step-by-step explanation:
Answer:
the answer is 1
Step-by-step explanation: i took the test hope this helps
5. A factory produces 1000 cans of juices in 5 days. How many cans will it produce in 15
days?
Answer:
3000
Step-by-step explanation:
3. In the expansion of (ax^2+ by)^8 the coefficients of last two terms are -5832 and 6561, respectively.
Find the values of: a and b
Answer:
a = -0.33
b = 3
Step-by-step explanation:
(ax²+ by)⁸
by the 8th level of Pascal Triangle, the coefficient of last 2 terms are
8 a*b⁷ = -5832 ... last 2nd term 8 ab⁷ x²y⁷
b⁸ = 6561 ... last term b⁸y⁸
b = 3
a = -5832/(8*3⁷) = -0.33
Can someone help me Expand 3(z+2)
Answer: 3z+6
Step-by-step explanation:
(3) (z+2)
(3) (z)+(3) (2)
3z+6
How does a woman being treated as a servant for a man show that equality between men and women is not being promoted?? PLS HELP; I’ll give brainliest :)
Answer:
because the woman is doing what the man tells her to and its not the other way around but it should be men and woman are either both servants or neither are servants
Step-by-step explanation:
Answer:
because woman were house wife's they took care of the meals for the family, take care of the children, and make things for the family
Step-by-step explanation:
10
−
3
x
=
−
2
(
x
+
4
)
Answer:
x = 18
Step-by-step explanation:
10 − 3x = − 2 (x + 4)
=> 10 − 3x = -2x - 8
=> x = 18
Hoped this helped.
Answer:
x = 18
Step-by-step explanation:
10 - 3x= -2(x+4)
First, we solve inside the parentheses.
10 - 3x= -2x - 8
Like terms:
-3x + 2x= -10 - 8
-x/-1 = -18/-1
x = 18
Two trains leave a train station traveling on parallel and adjacent tracks. Train A is traveling due north at a constant speed of 76 miles per hour. Train B is traveling due south at a constant speed of 44 miles per hour. If both trains leave the station at the same time, in approximately how many minutes will the trains be 22 miles apart? O 11 O 18 O 60 o 98
Answer:
TWO TRAINS IM SORRY LOLLL
Answer:
18 minutes
Step-by-step explanation:
Use the graph to complete the statements.
The car gets
30
miles to the gallon.
After the car has traveled?
miles, 2 and two-thirds how many gallons of gas have been consumed.
Answer:
The answer is 80 miles 2/23
Step-by-step explanation:
I hope this helps
expand and simplify in its simplest form (x+7)(x-2)
Answer:
[tex](x + 7) - (x - 2)[/tex]
x²-2x+7x-14
Answer:
x2+5x-14
Step-by-step explanation:
I wmat to sleep been doing work for an hour help me out
Answer:
A. 23, 37.....
B. 26, 42......
Step-by-step explanation:
have a great day!
What is the length of the hypotenuse? If necessary, round to the nearest tenth.
Answer:
17
Step-by-step explanation:
Answer:
The hypotenuse is 17.
Step-by-step explanation:
a^2+b^2=c^2.
Let's plug in a and b.
15^2 + 8^2 = c^2
Simply.
225+64=c^2
Add.
289=c^2.
Square 289 and c^2 to cancel out the ^2.
17=c
The hypotenuse is 17.
Hope I helped. :)
lf the volume of a sphere= 4.5π cm³ then the radius length is .....?
Answer:
Radius = 3.232 cm to the nearest thousandth.
Step-by-step explanation:
Volume of a sphere = 4/3πr^3, so:
45π = 4/3πr^3 π is common to both sides, so:
45 = 4/3 r^3
r^3 = 45 * 3/4
r^3 = 33.75
r = 3.232 cm.
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options.
x2 + (y – 3)2 = 36
x2 + (y – 5)2 = 6
(x – 4)² + y² = 36
(x + 6)² + y² = 144
x2 + (y + 8)2 = 36
Answer:
x2 + (y + 8)2 = 36
Step-by-step explanation:
:) took the test
The equations which represent circles that have a diameter of 12 units and a center that lies on the y-axis are x² + (y – 3)² = 36 and x² + (y + 8)² = 36.
What is the Standard form of a Circle?Standard form of a circle is given by the equation,
(x - h)² + (y - k)² = r²
where, (h, k) is the center of the circle and r is the radius of the circle.
Given that,
A circle has a diameter of 12 units.
So radius = 12 / 2 = 6 units
Center of the circle lies on the Y axis.
So the x coordinate of the center of the circle will be 0.
So, in (h, k), h = 0
So the equation will be of the form,
(x - 0)² + (y - k)² = 6²
x² + (y - k)² = 36
Hence the options are x² + (y – 3)² = 36 and x² + (y + 8)² = 36.
Learn more about Equations of Circles here :
https://brainly.com/question/29288238
#SPJ7
help me please
Explain what you would do first to simplify the expression below. Justify why, and then state the result of performing this step.
First clear the bracket of the inner fraction's numerator. This would allow you to reduce the inner fraction to lowest terms.
Given the expression
[tex](\frac{(2r^2t)^3}{4t^2})^2[/tex]
In order to simplify, note that the numerator and denominator of the fraction
[tex]\frac{(2r^2t)^3}{4t^2}[/tex]
have common factors. So, we would first remove the bracket in the numerator. This would allow us to reduce the fraction to lowest terms.
To clear the numerator's bracket, note that
[tex](2r^2t)^3=(2r^2t)\times(2r^2t)\times(2r^2t)\\=(2\times2\times2)\times(r^2\times r^2\times r^2)\times(t\times t\times t)\\=8\times r^6 \times t^3=8r^6 t^3[/tex]
that was long. The shorter way was to do the following
[tex](2r^2t)^3=2^3\times r^{2\times3}\times t^3=8r^6t^3[/tex]
so back to the original question, to simplify
[tex](\frac{(2r^2t)^3}{4t^2})^2[/tex]
we would do
[tex](\frac{(2r^2t)^3}{4t^2})^2=(\frac{2^3r^{2\times3}t^3}{4t^2})^2\\\\=(\frac{8r^6t^3}{4t^2})^2[/tex]
Now that we have removed the bracket from the numerator, we can now accomplish the step of reducing the fraction to lowest terms
[tex](\frac{8r^6t^3}{4t^2})^2=(\frac{8}{4}\times r^6\times \frac{t^3}{t^2})^2\\=(2\times r^6\times t^{3-2})^2\\=(2\times r^6\times t^1)^2\\=(2r^6t)^2[/tex]
Learn more here: https://brainly.com/question/1382660
