Answer:
a) s = 0.4
b) Z = 2.5
c) 99th percentile.
d) The larger sample size would lead to a smaller margin of error, which would lead to a higher z-score and a increased percentile.
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.
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.
Assume the average height for American women is 64 inches with a standard deviation of 2 inches
This means that [tex]\mu = 64, \sigma = 2[/tex]
A) Calculate the standard error for the distribution of means.
Sample of 25 means that [tex]n = 25[/tex], so [tex]s = \frac{2}{\sqrt{25}} = 0.4[/tex].
B) Calculate the z statistic for the sorority group.
Sample mean of 65 means that [tex]X = 65[/tex].
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{0.4}[/tex]
[tex]Z = \frac{65 - 64}{0.4}[/tex]
[tex]Z = 2.5[/tex]
C) What is the approximate percentile for this sample? Enter as a whole number.
Z = 2.5 has a p-value of 0.9938, so 0.99*100 = 99th percentile.
D) If the sorority actually had 36 members (still with an average of 65 inches), would you expect the percentile value to increase or decrease? why?
The larger sample size would lead to a smaller margin of error, which would lead to a higher z-score and a increased percentile.
Consider this linear function:
y= 1/2x+1.
Plot all ordered pairs for the values in the domain.
D: {-8, -4, 0, 2, 6}
Answer:
(-8,-3)
(-4,-1)
(0,1)
(2,2)
(6,4)
Step-by-step explanation:
One by one, substitue the x values and solve for y
Answer:
negative 4
Step-by-step explanation:
go
PLEASE HELP ME!! Kevin earns a base salary of $350.00 every week with an additional 12%
commission on everything he sells. If Kevin sold $4950.00 worth of items
last week, what was his total pay?
============================================================
Explanation:
He sold $4950 worth of items. Take 12% of this amount to get
12% of 4950 = 0.12*4950 = 594
So he earns $594 in commission on top of the $350 base salary paid every week. In total, he earns 594+350 = 944 dollars for that week
This isn't the per week pay because he would need to sell exactly $4950 worth of goods each week to keep this same weekly pay.
The monthly family income of a family is $15,000. They spend 28% of their monthly income on food. How much do they spend on food each month?
Answer - $
(fill in the value)
Answer:
$1000 each month.
Step-by-step explanation:
$1000 because 12 month and 1 month=$1000 the family have $3000.
What is the volume of the sphere m? Round your answer to the nearest hundredth
Answer:
below
Step-by-step explanation:
x = 8 *sin45
x =5.657
r = x = 5.657 in
v = 4/3πr³
v = 4/3 * 3.142*(5.657)³
v= 758.41 in
Answer:
758.25 in.^3
Step-by-step explanation:
a^2 + b^2 = c^2
2a^2 = 64
a^2 = 32
a = sqrt(32)
V = (4/3)(pi)r^3
V = (4/3)(3.141592654)(5.6568542459)^3
V = 758.25 in.^3
What is photosynthesis?
▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓[tex]\pmb{\qquad{\qquad{\underline{\green{\underline{\sf{Photosynthesis}}}}}}}[/tex]
Photosynthesis is the process by which green plants take in carbon dioxide and water, in the presence of chlorophyll by using sunlight to make their own food. Oxygen is released as a by product.
Chemical Reaction for PHOTOSYNTHESIS:
[tex]\sf 12H_2O + 6CO_2 \underset{chlorophyll}{\xrightarrow{Sunlight}} C_6H_{12}O_6 + 6H_2O + 6O_2 \uparrow[/tex]▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓
Triangle ABC is a right triangle.
The lengths of one leg is 60 feet, and the hypotenuse is 61 feet.
What is the length, in feet, of the other leg?
Answer:
Hello! answer: 11
Step-by-step explanation:
60 × 60 = 3600
11 × 11 = 121
3600 + 121 = 3721
√3721 = 61
therefore 11 is the missing leg Hope that helps!
Can y’all help me solve this question it’s due by the end of the day and I’m failing math?explain it plz
Answer:
x=4 and y=−4
Step-by-step explanation:
Let's solve your system by elimination.
−x−2y=4;3x+2y=4
−x−2y=4
3x+2y=4
Add these equations to eliminate y:
2x=8
Then solve 2x=8 for x:
2x=8
2x
2
=
8
2
(Divide both sides by 2)
x=4
Now that we've found x let's plug it back in to solve for y.
Write down an original equation:
−x−2y=4
Substitute 4 for x in−x−2y=4:
−4−2y=4
−2y−4=4(Simplify both sides of the equation)
−2y−4+4=4+4(Add 4 to both sides)
−2y=8
−2y
−2
=
8
−2
(Divide both sides by -2)
y=−4
I have a large money box, about 10 inches wide and 5 inches tall. Roughly, how many coins can I place in my empty money box?"
Answer:
Overall, it depends what type of coin you are using because each ones size is different. Or, if you are referring to the riddle it will be just one coin.
The correct answer is approximately 3,968 coins can be placed in the empty money box based on estimation. Based on these calculations, you can roughly estimate a volume calculation that place around 7936 coins in your empty money box, assuming the coins are similar in size to a quarter.
To estimate the number of coins that can fit in your money box, we need to consider the volume of the box and the volume of a single coin.
Calculate the volume of the money box:
Volume = Length * Width * Height
Volume = 10 inches * 10 inches * 5 inches
Volume = 500 cubic inches
Estimate the volume of a single coin. Let's assume a common coin, such as a quarter:
Diameter of a quarter ≈ 0.96 inches
Thickness of a quarter ≈ 0.07 inches
Volume of a coin ≈ π * ([tex]radius^2[/tex]) * thickness
Volume of a quarter ≈[tex]3.14 * (0.48) ^2 * 0.07[/tex]inches
Volume of a quarter ≈ 0.063 cubic inches
Calculate the number of coins that can fit in the money box:
Number of coins ≈ Volume of the money box / Volume of a coin
Number of coins ≈ 500 cubic inches / 0.063 cubic inches
Number of coins ≈ 7936 coins (approximately)
Therefore, approximately 3,968 coins can be placed in the empty money box based on estimation. Based on these calculations, you can roughly estimate a volume calculation that place around 7936 coins in your empty money box, assuming the coins are similar in size to a quarter.
Learn more about volume and estimations here:
https://brainly.com/question/20664459
#SPJ2
PLEASE HELP QUICK
Factor out the GCF of 14x4 + 21x2 + 28x
Answer:
14×4+21×2+28=126
Step-by-step explanation:
correct me if I'm wrong
What is the midpoint of the segment shown below?
(-2,4) (6,-4)
A. (3, 0)
B. (1, 0)
C. (4, 0)
D. (2, 0)
a p e x :(
Answer:
answer is option D
Step-by-step explanation:
(-2 , 4) = (x1 , y1)
(6 , -4) = (x2 , y2)
midpoint = (x1 + x2/2 , y1 + y2/2)
=(-2 +6/2 , 4+(-4)/2)
=(4/2 , 0/2)
=(2 , 0)
(5x20)+(8x10) PLEASE HELP
Answer:
180
Step-by-step explanation:
5*20 is 100. 10 *8 is 80. then you add
Gregory knows that ABC is reflected onto A'B'C. Which statement about the figures is true? Olf Gregory draws the segment with endpoints A and A', then the midpoint will lie on the line of reflection O If Gregory draws the segment with endpoints B and C', then the midpoint will be on the line of reflection O Points A and B are equidistant from the line of reflection O AB will be perpendicular to the line of reflection
The true statement about the reflection is (a) If Gregory draws the segment with endpoints A and A’, then the midpoint will lie on the line of reflection.
When a shape is reflected, it must be reflected across a line (called the line of reflection)
The line of reflection is always located at a point equidistant to the image and the pre-image of the shape that is being reflected
Hence, the true statement is (a) If Gregory draws the segment with endpoints A and A’, then the midpoint will lie on the line of reflection.
Read more about reflection at:
https://brainly.com/question/4289712
Answer:
a
Step-by-step explanation:
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Look at the triangle below which of the following represents two of the angle measures of the triangle
Answer:
x = 7
two of the angles 60 and 80
Step-by-step explanation:
The sum of interior angles in a triangle is equal to 180
8x + 4 + 6x - 2 + 10x + 10 = 180 add like terms
24x + 12 = 180 subtract 12 from both sides
24x = 168 divide both sides by 24
x = 7 replace x with 7 in the equation to find the angle measures
6x - 2 = 40
10x + 10 = 80
8x + 4 = 60
Pat used unit cubes to build a right rectangular prism with a volume of 32 cubic units. The height of the prism is 4 units. What figure could be the bottom layer of the prism?
Answer:
It must be a rectangle with dimension of either 1 by 8 or 2 by 4
Step-by-step explanation:
V = l*w*h
32 = l*w*4
32/4 = l*w*4/4
8 = l*w
We could have 1*8
We could have 2*4
It must be a rectangle
It must be a rectangle with dimension of either 1 by 8 or 2 by 4
Please help and don’t give links
Answer:
B.d.c.b.a.c.b is. respectively answer
1 Which set of ordered pairs does not represent a function?
1 {(1, 10), (3, 18), (5, 26), (7, 34), (9, 42)
2 {(2, 10), (3, 20), (4, 15), (5,5), (6,25)
3 {(0,8), (5,4), (10,0), (15, 4), (20,8)
4 {(9, 1), (6,2), (3, 3), (6,4), (9,5)}
Faisal tries to solve
(x + 2)(x - 7) = 0
Here is his working.
(x + 2) = 0
or
(x - 7) = 0
Answer
x = 2
or
x=7
Give a reason why his answer is wrong.
Answer:
He should have subtracted 2 from each side to find the solution for x+2 =0
Step-by-step explanation:
(x + 2)(x - 7) = 0
Using the zero product property
x+2 = 0 x-7=0
x+2-2=0-2 x-7+7=0+7
x = -2 x=7
He should have subtracted 2 from each side to find the solution for x+2 =0
Step-by-step explanation:
the steps he took are correct but the answer of x is somehow wrong because
(x+2)=0
x = -2
and not x = 2
Maria earns 13 dollars each hour working part-time at a bookstore. She earns one additional dollar for each book that she sells.
Let A be the amount (in dollars) that Maria earns in an hour if she sells B books.
Write an equation relating A to B. Then graph your equation using the axes below.
Answer:
a = 13 + b
Step-by-step explanation:
2/3 feet is how many inches
Answer:
(2/3) foot = 8 inches
Need these written in standard form!
HELPPPPPPPP 17 PTSSSSSSSSSSSSSSSSSS
Answer:
A: 360
Step-by-step explanation:
Split the trapezoid into 2 shapes
Then find the area of the rectangle on the left:
18 × 15 = 270 square yards
Now for the triangle, first find the base by subtracting the 2 parallel lines:
25 - 15 = 10 yards
0.5(10 × 18) = 90 square yards
Add both areas to find total area:
270 + 90 = 360 square yards
All this can be seen in the figure below:
PLS PLS ANSWER SOMEONE
Answer:
the answer i think it is 5
im not 100% sure on what the question is, but i hope this helps
Step-by-step explanation:
Solve the formula Ax + By = C for A.
Answer:
A=C/x-By/x
Step-by-step explanation:
Lisa rectangular living room is 20 feet wide if the length is 6 feet less than twice the width what is the area of a living room
Answer:
Step-by-step explanation:
20 * ((2*20)-6)
20*34
680
Help ill give brainliest
Answer:
$28.68
Step-by-step explanation:
57.24+64.08
121.32
150-121.32
Can anyone solve this?
Answer:
They are congruent
Step-by-step explanation:
The reason that WK is congruent to WL is because both come from the same origin of W and they both end up in the same place on their side. Which means if WK and WL are congruent, that means that AK and AL are congruent as well.
5
What are the necessary edena ton she lobe
prestetichet to the givetiline and have the satte
itet
4
o the shape is an edheners the fronta (0,2)
O the Made is - and contents the trenta (0,7)
O the shenues its ? and Enhas the faith (0,2))
o the meanser ve and ententies the fat (0,2)
6
Help me
Answer
6
Step-by-step explanation:
help omg, it would suck if anyone with big mommy milkers can teach me the answer
Answer:
Is it a square? If so, then the other side would be a 98 since all sides in a square are equal
Step-by-step explanation:
2/5=2÷[blank]
fill in the blank.
Answer:
5
Step-by-step explanation:
2/5 is the same thing as 2÷5 since / and ÷ both mean to divide. So therefore your blank would be 5.
Given that r= 2p2/q-3 ; rearrange the formula to make q the subject of the formula.
Step-by-step explanation:
The given expression is:
[tex]r=\dfrac{2p^2}{q-3}[/tex]
We need to solve it to make q the subject of the formula.
Cross multiplying both sides,
[tex]rq-3r=2p^2[/tex]
Adding 3r to both sides,
[tex]rq-3r+3r=2p^2+3r\\\\rq=2p^2+3r[/tex]
Now, dividing both sides by r,
[tex]q=\dfrac{2p^2+3r}{r}[/tex]
Hence, this is the required solution.
