Answer:
a) 0.1151 = 11.51% probability that an individual distance is greater than 210.00 cm.
b) 0.883 = 88.3% probability that the mean for 20 randomly selected distances is greater than 197.80 cm.
c) The distribution of the population is normal, which means that the sample size does not need to exceed 30.
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 zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
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.
The overhead reach distances of adult females are normally distributed with a mean of 200 cm and a standard deviation of 8.3 cm.
This means that [tex]\mu = 200, \sigma = 8.3[/tex]
a. Find the probability that an individual distance is greater than 210.00 cm.
This is 1 subtracted by the pvalue of Z when X = 210. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{210 - 200}{8.3}[/tex]
[tex]Z = 1.2[/tex]
[tex]Z = 1.2[/tex] has a pvalue of 0.8849
1 - 0.8849 = 0.1151
0.1151 = 11.51% probability that an individual distance is greater than 210.00 cm.
b. Find the probability that the mean for 20 randomly selected distances is greater than 197.80 cm
Now [tex]n = 20, s = \frac{8.3}{\sqrt{20}} = 1.8559[/tex]
This probability is 1 subtracted by the pvalue of Z when X = 197.8. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{197.8 - 200}{1.8559}[/tex]
[tex]Z = -1.19[/tex]
[tex]Z = -1.19[/tex] has a pvalue of 0.117
1 - 0.117 = 0.883
0.883 = 88.3% probability that the mean for 20 randomly selected distances is greater than 197.80 cm.
c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?
The distribution of the population is normal, which means that the sample size does not need to exceed 30.
What is the percent increase from 50 to 74?
Answer:
67.57%
Step-by-step explanation: 50 is 67.57% of 74.
9. The radius of sphere is increasing at a rate of 3cm/minute. Find the rate of change of volume
when r=2cm *
V = 12
48л
16л
64 л
32T
Answer:
48π
Step-by-step explanation:
Given that,
The radius of the sphere is increasing at a rate of 3cm/minute, [tex]\dfrac{dr}{dt}=3\ cm/minute[/tex]
The volume of a sphere is given by :
[tex]V=\dfrac{4}{3}\pi r^3[/tex]
Differentiating both sides wrt t.
[tex]\dfrac{dV}{dt}=\dfrac{4}{3}\pi \times 3r^2\times \dfrac{dr}{dt}\\\\=4\pi r^2\times \dfrac{dr}{dt}[/tex]
Put r = 2 cm and dr/dt = 3 cm/minute
So,
[tex]\dfrac{dV}{dt}=4\pi r^2\times \dfrac{dr}{dt}\\\\\dfrac{dV}{dt}=4\pi \times 2^2\times 3\\\\\dfrac{dV}{dt}=48\pi[/tex]
Hence, the correct option is (a) "48π".
Help I would appreciate it
Answer:
it is option C
hope it helps
97 And 83
PLEASE ANSWER ASAP FOR BRAINLEST!!!!!!!!!!!!!!!!!!!!!!!
Answer:
400 units
Step-by-step explanation:
15 cm per 3 units which is 5 cm per 1 unit
80 times 5 is 400
Can someone please help me.
Sam finished 5/6 of his homework, John finished 3/4 of his homework, and Tom finished 10/12 of his homework. Which two students finished the same amount of homework?
Answer:
Sam and Tom
Step-by-step explanation:
5 × 2= 10
6 × 2= 12
5/6= 10/12
Jake needs a new camera for school. He has already saved $110 and he earns $9 per hour in a photography internship.
If the equation s = 9h + 110 represents that relationship, how many hours will he need to work (h) in order to save (s) $425 to purchase
his camera?
Help
Please help me find this
Answer:
i think 178 or 156
Step-by-step explanation:
10x6= 60
6x8=48
6x8=48
6x5=35
add all answers= 191
CaN Someone PLEAAASSEEE HELP ME!!!!!
Answer:
A or B , whether it is dotted or straight line dunno
PLEASE HELP NOBODY KNOWS ? Mhmh
Answer:
76%
Step-by-step explanation:
Times the decimal by 100 to get a percent
basically moving the decimal 2 spaces to the right.
URGENT GEOMETRY!!! can someone help me with this please
Answer:
To find the angle of this triangle you have to [tex]cos^{-1}(\frac{4.87}{5.35})[/tex]. When you do this you will get 24 as the angle
Step-by-step explanation:
Hope this Helped
WILL GIVE BRAINLYIST
Answer:
64 degrees
Step-by-step explanation:
Since the triangles are similar they have the same angle measures
[tex]\frac{PR}{PQ} =\frac{SU}{ST}[/tex] [tex]\frac{21}{14}= \frac{6}{4}[/tex]
∠P = ∠S ∠R =∠U ∠Q=∠T
We know 2 of the angle measures: ∠S and ∠R, and since they are similar we know ∠P and ∠U
In triangles the sum of all angle measures is always 180 degrees, so we can solve for ∠Q with this formula
[tex]A+B+C=180[/tex]
[tex]46+70+C+180[/tex]
[tex]116+C=180[/tex]
subtract 116 from both sides
[tex]C=64[/tex]
Therefore ∠Q is equal to 64 degrees
It takes Phillip 11 hours to proof read a chapter of hawked learning systems college algebra book and it takes Cynthia 4 hours. how long would it take them working together?
if x=4y then what percentage of 2x is 2y
Answer:
x=2y
2x=4y
percent=(2y/2x)*100%=(x/2x)*100%=50%
Answer:
the answer to this question would be 50%
is 20% greater or less than 1/4
Answer: 20% is less than 1/4
Step-by-step explanation:
1/4 is 25%
25%> 20%
Answer: less
Step-by-step explanation:
Move the sliders to set the values of r, h, and k, and record at least three different sets of data. Also record the equations of the corresponding circles.
Answer: Hope this helps! xx have a good day!
Step-by-step explanation:
The equations of the corresponding circles can be any equation only have to satisfy the general equation for circle .
What is general equation of circle?A circle is the set of all points in a plane at a given distance (called the radius ) from a given point (called the center.)
We know that the general equation for a circle is
[tex]( x - h )^2 + ( y - k )^2 = r^2[/tex],
where ( h, k ) is the center and r is the radius.
According to the question
The equation of circle given is
[tex]x^{2} + y^{2} = 1[/tex]
Center at origin
i.e
(h,k) = (0,0)
and radius = 1 unit
Now ,
By changing changing center (h,k) and radius of equation it will give following equations
h k r equation of circle
0 1 3 [tex]( x - 0 )^2 + ( y - 1 )^2 = 3^2[/tex]
2 2 3 [tex]( x - 2 )^2 + ( y - 2)^2 = 3^2[/tex]
1 1 1 [tex]( x - 1 )^2 + ( y - 1 )^2 = 1^2[/tex]
-2 -1 2 [tex]( x +2 )^2 + ( y + 1 )^2 = 2^2[/tex]
3 2 1 [tex]( x - 3 )^2 + ( y - 2 )^2 = 1^2[/tex]
-5 1 3 [tex]( x +5 )^2 + ( y - 1 )^2 = 3^2[/tex]
Hence, the equations of the corresponding circles can be any equation only have to satisfy the general equation for circle .
To know more about general equation for a circle here:
https://brainly.com/question/10618691
#SPJ2
The Blinking Rockets baseball team has had 127,034 visitors to their fan website. Rounded to the nearest ten thousand how many visitors have they had
Answer:
[tex]Visitors = 130000[/tex]
Step-by-step explanation:
Given
[tex]Visitors = 127034[/tex]
Required
Approximate to the nearest ten thousand
First, identify the digit at the ten thousand position
From the given numbers of visitors, the digit is 2.
So, the next digit (which is 7) will be approximated and added to 2.
7 > 5. So, 1 will be added to 2.
The number of visitors becomes:
[tex]Visitors = 130000[/tex]
factor if posible X/2-4X-12
Answer:
Please refer to the attachment
Answer:
3. (x + 6)(x + 3)
4. (x-6)(x+2)
Step-by-step explanation:
3. x^2 + 9x + 18
To check if it is factorable, first check the discriminant
b^2 - 4ac
9^2 - 4(1)(18)
81 - 72
9
Since D > 0, there are real number solutions
Now let us try and factor
Find a number that adds to 9 and multiplies to 18
3 and 6 work
Rewrite the equation as
x^2 + 3x + 6x + 18
x(x + 3) + 6(x + 3)
(x + 6)(x + 3)
4. x^2 - 4x - 12
To check if it is factorable, first check the discriminant
b^2 - 4ac
(-4)^2 - 4(1)(-12)
16 + 48 = 64
Since D > 0, there are real number solutions
Now let us try and factor
Find a number that adds to -4 and multiplies to -12
-6 and 2 work
Rewrite the equation as
x^2 - 6x + 2x - 12
x(x - 6) + 2(x - 6)
(x + 2)(x - 6)
Can someone please help me
Answer
7 and 83
Step-by-step explanation:
Can someone answer and explain ill mark brainliest
Answer:
56 of the coins are dimes
Step-by-step explanation:
Dimes = D
Quarters = Q
D+Q=102
10D+25Q=1710
-10(D+Q=102)
-10D-10Q=-1020
+10D+25Q=1710
15Q-690
Q=46
D=102-46=56
CHECK 46(25)+56(10)=1150+560=1710 = YES
So if the value of the solid's surface area is equal to the volume. Find the value of x
The height of the solid is 5in and the width is 6in. X is the value of the length
Answer:The solid surface area is equal to the solid volume. Find the value of x? The measurements of the rectangular prism is 11 inches long and 3 inches wide. Height is not listed.
The height of the solid is 5in and the width is 6in. X is the value of the length
4
Step-by-step explanation:
1651.43 rounded to the nearest hundred
Answer:
1600
Step-by-step explanation:
Aldos coffee shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Aldo $4.15 per pound, and type of B coffee costs $5.25 per pound. This month, Aldo made 119 pounds of the blend, for a total cost of $548.85. How many pounds of type B coffee did he use?
Let A represent amount of Type A coffee pounds used.
Let B represent amount of Type B coffee pounds used
A + B = 156
B = 156 - A
A = 156 - B
5.80A + 4.65B = 826.60
580 (156 - B) + 4.65B - 826.60 = 0
904.8 - 5.80B + 4.65B - 826.60 = 0
904.8 - 1.15B - 826.60 = 0
78.2 - 1.15B = 0
78.2/1.15 = 1.15B/1.15
68 = B
B = 68 pounds of Type B coffee
There's many more steps you can take to check and etc but am too lazy to put down sorry.
There has been much media coverage of the high cost of medicinal drugs in the United States. One concern is the large variation from pharmacy to pharmacy. To investigate, a consumer advocacy group took a random sample of 100 pharmacies around the country and recorded the price (in dollars per 100 pills) of Prozac. Compute the range, variance, and standard deviation of the prices. Discuss what these statistics tell you.
Data for the question :
102.05 99.85 112.3 97.15 111.23 105.37 105.64 106.5 102.97 107.82 106.36 111.24 107.28 114.14 106.28 106.96 98.25 111.55 107.75 101.02 101.12 97.7 97.66 100.54 115.77 112.91 111.04 112.15 102.87 101.14 107.13 108.56 109.56 103.57 108.68 104.59 116.74 116.22 100.22 103.97 111.2 109.34 115.78 101.59 107.93 104.23 96.25 103.84 102.47 102.96 99.26 101.42 108.58 107.69 99.88 102.71 111.25 99.4 117.04 106.35 110.44 102.34 107.25 107.63 105.2 109.14 115.54 101.51 108.49 112.32 109.27 97.54 102.46 105.94 109.42 111.05 102.63 106.99 102.03 108.84 118.8 108.64 95.35 105.47 104.45 102.15 111.4 108.27 104.82 108.4 109.05 116.11 103.7 121.2 99.62 102.81 109.56 103.35 113.02 103.79
Answer:
Range = 25.35
Variance = 29.46
Standard deviation = 5.43
The variation in price of Prozac is high
Step-by-step explanation:
The range of the data :
Maximum - Minimum.
121.2 - 95.35 = 25.35
The variance, s :
s² = Σ(X - m²) / n - 1
Mean, m = Σx / n
X = individual data point
m = mean of data
n = sample size
Using a calculator of save time and ensure accuracy :
s² = 29.45522
The standard deviation, s
s = sqrt(variance)
s = sqrt(s²)
s = sqrt(29.45522)
s = 5.42726.
The range, variance and standard deviation, all measure the degree of variation in a dataset. The values of these statistical measure obtain for the price of 1 product across different pharmaceutical stores, suggests thatvthe variation in price is high;
With a range of about 25.35 and standard deviation of 5.43
what is the square root of 25? =7
Answer: 625
Step-by-step explanation:
In Vedic mathematics, the numbers containing 5 in the units place can be squared by taking the remaining digit/s and multiply by its successor and then add 25.
Square of 25 is 2*3 = 6 and attach 25, So 25^2 = 625.
Square of 35 is 3*4 = 12 and attach 25, So 35^2 = 1225.
Square of 125 is 12*13 = 156 and attach 25, So 125^2 = 15625.
Square of 95 is 9*10 = 90 and attach 25, So 95^2 = 9025.
From the time I had answered the question asking for the square of 25, the question now appears as what is the square root of 25.
I will answer the revised question as square root of 25 is +5 or -5.
¿Qué porcentaje de niños prefieren la materia de español? Considera que los 9 alumnos son igual al 100 %?
Answer:
hold yo ablo espanol
Step-by-step explanation:
HELP THIS WAS DUE THREE DAYS AGO!!!!!!!!!!
Answer:
Step-by-step explanation:
2. 2c(7c + 1)
3. stays as is
4. 2x^3y^4(4 - 11x^2y^2)
5. ab(10ab + 9b - a)
6. 3m^2(7m^4n^2+2m^2n+5)
7. (a - 8)(a + 8)
8. (y - 17)(y + 17)
9. stays as is
10. (1 - 5n)(1 + 5n)
11. (4x - 7y)(4x + 7y)
12. (w^2 - 10)(w^2 + 10)
13. (c - 9d)(c + 9d)
14. (14a - b)(14a + b)
PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA 40 POINTS* DONT SKIP :(( .!
Answer:
no solution
Step-by-step explanation:
Answer:
One solution
Step-by-step explanation:
(1288/1935, 236/387)
select the correct anwser from the drop down menu.
what equation has no solution
A. 13y + 2-2y = 10y + 3 - y
B. 9 (3y + 7) - 2 = 3 ( - 9y + 9)
C. 32.1y + 3.1 + 2.4y - 8.2 = 34.5y - 5.1
D. 5 (2.2y + 3.4) = 5 (y - 2) + 6y
Answer:
D. 5(2.2y + 3.4) = 5(y-2) + 6y
This equation has no solution
Find the measure of AB *
14 cm
24 cm
10 cm
140 cm
Answer:
10 cm
Step-by-step explanation:
Because it is a parrallogram and by its property it will be 10