Solution :
Given :
p = 12% = 0.12
n = 15..
Mean is defined as the product of a sample size n and the probability p such that :
[tex]$\mu_X = np = 1500 \times 0.12$[/tex]
= 180
Standard deviation may be defined as the square of a product of the sample size n, the probability p and the probability 1-p :
[tex]$\sigma_X = \sqrt{np(1-p)}$[/tex]
[tex]$\sigma_X = \sqrt{1500 \times 0.12 \times (1-0.12)}$[/tex]
≈ 12.5857
The z-score is given by :
[tex]$z=\frac {x- \mu}{\sigma } $[/tex]
[tex]$z=\frac {165-180} {12.5857 }$[/tex]
≈ -1.19
[tex]$z=\frac {x- \mu}{\sigma } $[/tex]
[tex]$z=\frac{195-180} {12.5857 }$[/tex]
≈ 1.19
Now determining the corresponding probability using table :
P (165 ≤ X ≤ 195 ) = P (-1.19 ≤ Z ≤ 1.19 )
= 1-2 x P(Z < -1.19)
= 1-2 x 0.1170
= 1-0.2340
= 0.7660
= 76.60%
Given values,
p = 12%= 0.12
n = 1500The mean will be
→ [tex]\mu x = np[/tex]
By putting the values,
[tex]= 1500\times 0.12[/tex]
[tex]= 180[/tex]
The standard deviation will be:
→ [tex]\sigma x = \sqrt{np(1-p)}[/tex]
[tex]= \sqrt{1500\times 0.12\times (1-0.12)}[/tex]
[tex]= 12.5857[/tex]
The z-score will be:
→ [tex]z = \frac{x- \mu}{\sigma}[/tex]
[tex]= \frac{165-180}{12.5857}[/tex]
[tex]= -1.19[/tex]
and,
→ [tex]z = \frac{195-180}{12.5857}[/tex]
[tex]= 1.19[/tex]
hence,
The probability will be:
→ [tex]P(165 \leq X \leq 195) = P(-1.19 \leq Z \leq 1.19)[/tex]
[tex]= 1-2\times P(Z < -1.19)[/tex]
[tex]= 1-2\times 0.1170[/tex]
[tex]= 1-0.2340[/tex]
[tex]= 0.7660[/tex]
[tex]= 76.60[/tex] (%)
Thus the answer above is right.
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if you want to build a ramp that is 20 ft long and 5ft tall what is the angle of elevation? draw a diagram to model the situation
Answer:
Step-by-step explanation:
64.16
Please help me with the question
Answer:
area = 84 m²
Step-by-step explanation:
area = (1/2)(4)(3)(2) + (5)(6) + (6)(3) + (4)(6) = 84 m²
find the sale price of the item. round to two decimal places if necessary original price $225.60 markdown 80 %
Answer:
gan if you could anssbdhe
Step-by-step explanation:
A birdbath holds 4 liters of water. How many milliliters does it hold?
Answer:
4000
Step-by-step explanation:
Answer:
4000
Step-by-step explanation:
You have to multiply the volume value by 1000. So 4 x 1000=4000
The diagram below shows a cone and a cylinder that have congruent bases and congruent heights.
2.5 in
2.5 in
4 in.
Which statement, where h represents the height of the cone and the height of the cylinder, is true?
its x of course :)))
Cora uses the following ingredients to make once more.
Answer:
10 if the other the numbers go up as well
Step-by-step explanation:
20/2= 10
Which would mean Kora could make 10 s'mores
What is the midpoint of a segment with endpoints at (-4, -8) and (8,10)
2. The area A of a circle is increasing at a constant rate of 2.5cm s . If the area of the circle is given
by A = πr2, what is the rate of change of the radius when the radius is 15cm?
Answer:
235.65 cm^2s-1
Step-by-step explanation:
We have that;
Rate of change of area (dA/dt) = (dA/dr) (dr/dt) By chain rule
Note that dr/dt = rate of change of radius
But
A = πr^2
dA/dr = 2πr
dr/dt = 2.5cm s-1 (given)
So;
dA/dt = 2πr * 2.5cm s-1
r = 15cm (given)
dA/dt = 2 * 3.142 * 15cm * 2.5cm s-1
dA/dt = 235.65 cm^2s-1
5. A book of length 20 cm and breadth 5 cm is kept on a table, its area is
(a) 50 cm
(b) 100 cm
(c) 150 cm
(d) 200 cm
Suppose that 8% of college students are vegetarians. Determine if the following statements are true or false, and explain your reasoning.
a. The distribution of the sample proportions of vegetarians in random samples of size 60 is approximately normal since n >= 30.
b. The distribution of the sample proportions of vegetarian college students in random samples of size 50 is right skewed.
c. A random sample of 125 college students where 12% are vegetarians would be considered unusual.
d. A random sample of 250 college students where 12% are vegetarians would be considered unusual.
e. The standard error would be reduced by one-half if we increased the sample size from 125 to 250.
Step-by-step explanation:
we have p=proportion of vegetarian students=0.08
a. FALSE.
for normal approximations we must have np>=5 and n(1-p)>=5
here n=60 so np=60*0.08=4.8 which is less than 5.
hence normal approximation is not applicable.
b. TRUE.
for binomial proportion , the distribution is right skewed if 1-2p>0 or, 0.5>p
here, p=0.08 so 0.5>p is satisfied. hence it is rightly skewed.
c. FALSE.
here, n=125 which is quite large. hence normal approximation is applicable.
let phat be the sample proportion
then phat approximately follows a normal distribution with E[phat]=p=0.08
and variance=V[phat]=p(1-p)/n=0.08(1-0.08)/125=0.0005888
hence standard deviation=sqrt(0.0005888)=0.0242652
hence effective range of phat is [0.08-3*0.0242652,0.08+3*0.0242652]=[0.0072044,0.1527956]
12%=0.12 lies in this effective range.
hence it is not unusual.
In this exercise we have to classify whether the statements are true or false:
a) False
b) True
c) False
d) False
e) False
We have: [tex]p=proportion of vegetarian students=0.08[/tex]
a) FALSE.
For normal approximations we must have:
[tex]np\geq 5 \\n(1-p)\geq 5[/tex]
Where [tex]n=60[/tex] so [tex]np=60*0.08=4.8[/tex] which is less than 5. Hence normal approximation is not applicable.
b)TRUE.
For binomial proportion , the distribution is right skewed if :
[tex]1-2p>0 \\ 0.5>p[/tex]
Where, p=0.08 so 0.5>p is satisfied. hence it is rightly skewed.
c) FALSE.
Where, n=125 which is quite large. hence normal approximation is applicable. Let phat be the sample proportion then phat approximately follows a normal distribution with:
[tex]E[phat]=p=0.08[/tex]
and [tex]variance=V[phat]=p(1-p)/n=0.08(1-0.08)/125=0.0005888[/tex]
Hence standard deviation [tex]=sqrt(0.0005888)=0.0242652[/tex]
hence effective range of phat is:
[tex][0.08-3*0.0242652,0.08+3*0.0242652]=[0.0072044,0.1527956][/tex]
12%=0.12 lies in this effective range. Hence it is not unusual.
d) FALSE.
e) FALSE.
See more about proportion at : brainly.com/question/8704765
6 times 10 to the power of -10 Normal numbers
Answer:
0.0000000006
Step-by-step explanation:
6* 10^-10= 0.0000000006
basically think of it as moving the decimal back 10 times.
List the kinds of measurements have you worked with so far. Describe what area is. Describe what volume is.
How could you find the combined area of all faces of a three-dimensional shape? Give an example of why that would be a good measurement to know.
Answer: length, width, and hight
hope this helps \(￣︶￣*\))
3x-4 3x-8 solve for x
Answer:
32
Step-by-step explanation:
(3x-4)+(3x-8)=180
6x-12=180
6x=192
X=32
Applying the concept of supplementary angles the value of x we get is 32.
Use the concept of supplementary angles defined as:
The pair of angles known as supplementary angles always add up to 180 degrees. The definition of the term "supplementary" is "something supplied to complete a thing." These two perspectives are therefore referred to be complements of one another.
The given angles are:
Exterior angle = 3x - 4
Interior angle = 3x-8
From the figure, we can see that,
These angles are supplementary angles.
And since we know two angles are supplementary angles then,
Their sum = 180 degrees.
Therefore,
3x - 4 + 3x-8 = 180
6x - 12 = 180
Add 12 both sides are,
6x = 192
Divide by 6 on both sides,
x = 32
Hence,
The value of x is 32.
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What is the factored form of this polynomial? x2 + 5x − 36
A. (x + 4)(x + 9)
B. (x − 4)(x − 9)
C. (x − 5)(x + 8)
D. (x − 4)(x + 9)
Answer:
D. (x - 4)(x + 9)
Step-by-step explanation:
x2+5x−36
[think of numbers that add together to get 5 and multiply together to get -36!]
-4 + 9 = 5
-4 * 9 = -36
hope this helped! :]
Answer:
D: ( x - 4 ) ( x + 9 )
Step-by-step explanation:
By multipling the two friction :
x2 + 9x - 4x - 36
= x2 + 5x - 36
The length of the rectangle is 9 cm.
The perimeter of the rectangle is 31 cm.
(b) Work out the width of the rectangle.
Answer:
Perimeter = 2(L+W)
31 =2(9+w)
31 =18+2W
31-18=2W
13=2W
W=13/2
W=6.5cm
You roll a fair die three times. What is the probability of each of the following? a) You roll all 2's. b) You roll all odd numbers. c) None of your rolls gets a number divisible by 3. d) You roll at least one 4. e) The numbers you roll are not all 4's.
Answer:
[tex]\frac{1}{6}[/tex]×[tex]\frac{1}{6}[/tex]×[tex]\frac{1}{6}[/tex][tex]=\frac{1}{72}[/tex]
[tex]\frac{1}{2}[/tex]×[tex]\frac{1}{2}[/tex]×[tex]\frac{1}{2} =\frac{2}{8}[/tex]
[tex]\frac{4}{6}[/tex]×[tex]\frac{4}{6}[/tex]×[tex]\frac{4}{6} =[/tex][tex]\frac{8}{27}[/tex]
[tex]\frac{1}{6}[/tex]×[tex]\frac{1}{6}[/tex]×[tex]\frac{1}{6}[/tex][tex]=\frac{1}{72}[/tex]
[tex]\frac{8}{27}[/tex]
PLEASE ANSWER ASAP FOR BRAINELST!!!!!!!!!!!!!!!!!!!
Find the area of the figure.
NO LINKS
PLZ ANSWER NO FAKE LINKS
Answer:
Draw a Rectangle with 3/10 at the bottom and 1/2 at the top
Step-by-step explanation:
Have a Nice Day!
Assume a normal distribution. From the Baltimore facility, 145 samples were obtained and compared with a sample of 128 from the Burlington facility. The mean hours per week and standard deviations for middle management who had been with the organizations for approximately the same length of time were:
Answer:
Hello your question has some missing part below is the missing part
The mean hours per week and standard deviations for middle management who had been with the organizations for approximately the same length of time were: Baltimore facility, Burlington facility Mean 52.5 Mean 39.7
Standard deviation 19.7 Standard Deviation 8.9Using this data, complete the following:
State your hypothesis and conduct a hypothesis testing using a significance of 0.10.
answer : We will reject the Null hypothesis
Step-by-step explanation:
μ1 = mean working hours for Baltimore facility
μ2 = mean working hours for Burlington facility
Hence the Hypothesis are :
H0 : μ1 = μ2
Ha : μ1 > μ2
Next: Conduct a hypothesis testing
we will apply Z - testing attached below is the hypothesis testing
n1 = 145 , X1 = 52.5 , δ1 = 19.7 ( Baltimore )
n2 = 128, X2 = 39.7 , δ2 = 8.9 ( Burlington )
A rectangle has length 5.5 meters and width 7.5 meters. Select the area of the rectangle.
Answer:
41.25
Step-by-step explanation:
(1) area = 5.5 × 7.5
(2) area = 41.25
:)
Answer:More than nine-in-ten Hispanics identify with a specific religion. That, along with several other measures of belief and behavior, means that Hispanics as a group are highly religious. How does this affinity for spirituality vary among Latinos with different demographic characteristics or religious affiliations? And how precisely do the religious beliefs of Latinos set them apart from the rest of the population?
Step-by-step explanation:
Help please will mark brainliest
Answer:
9.9
Step-by-step explanation:
4.8 x 2 = 9.6
29.5 - 9.6 = 19.9
19.9/2 = 9.95
round up
9.9
Answer:
10 I think
Step-by-step explanation:
A polynomial function contains the factors x, x - 3 , and x + 1 Which graphs could represent the polynomial function? SELECT ALL THAT APPLY.
Answer:
Option B and F.
Step-by-step explanation:
Given that the terms x, x-3 and x+1, are the factors of the polynomial, therefore the roots are calculated by equating the factors to zero,
[tex]x = 0[/tex]
x - 3 = 0 ➡️ x = 3
x + 1 ➡️ x = -1
Plus, the polynomial has the zeroes -1, 0 and 3.
It means that the curve of the graph should intersect the x-axis at x = 0, x = 1, and x = 3.
Now select the graphs which pass through (-1, 0), (0, 0) and (3, 0).
It is observed that the graphs in options B and F follow this path.
So the correct choices are option B and F.
Sam borrows R7000 from a Bank at 14% p.a ,simple interest for 5 years.
How much does he have to pay back to the Bank at the end of 5 years period.
Answer:
$ 4,900.00
Step-by-step explanation:
I = 7000 × 0.14 × 5 = 4900
I = $ 4,900.00
A spinner has six equal-sized sections numbered 1, 1, 2, 2, 3, and 4. What is the probability of spinning a 3?
Answer:
1/6 or 0.166666...
Step-by-step explanation:
1 out of 6, so 1/6
10×2+5÷2
its so easy
Answer:
10×2+ 5÷2
=20+2.5
=22.5
The ratio of girls to boys in a boarding school is 2:7,if there are 1251 student in the school, how many of the student are girls
278 students are girls in this case.
need help ASAP plssssssssssssssssss
3,945 ÷ 45 = (?)
R (?)
Choose all the possible solution that makes the inequality statement True
x + 15 ≤ 35
O 20, 21, 22
O 18, 19, 20
O -18,-19,-20
O 50, 51, 52
Answer:
18, 19, 20
-18,-19,-20
Step-by-step explanation:
x + 15 ≤ 35
x ≤ 35 - 15
x ≤ 20
x must be 20 or less than it
PLEASE HELP I WILL MARK YOU BRAINIEST
A cylinder has a height of 15 millimeters. Its volume is 10,597.5 cubic millimeters. What is the
radius of the cylinder?
Answer: 15
Step-by-step explanation: r=V
πh=10597.5
π·15≈14.9962