Answer:
Explained below.
Step-by-step explanation:
According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.
The mean of this sampling distribution of sample proportion is:
[tex]\mu_{\hat p}= p[/tex]
The standard deviation of this sampling distribution of sample proportion is:
[tex]\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}[/tex]
(a)
The sample selected is of size n = 450 > 30.
Then according to the central limit theorem the sampling distribution of sample proportion is normally distributed.
The mean and standard deviation are:
[tex]\mu_{\hat p}=p=0.75\\\\\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.75(1-0.75)}{450}}=0.0204[/tex]
So, the sampling distribution of sample proportion is [tex]\hat p\sim N(0.75,0.0204^{2})[/tex].
(b)
Compute the probability that the sample proportion will be within 0.04 of the population proportion as follows:
[tex]P(p-0.04<\hat p<p+0.04)=P(\frac{-0.04}{0.0204}<\frac{\hat p-p}{\sigma_{\hat p}}<\frac{0.04}{0.0204})[/tex]
[tex]=P(-1.96<Z<196)\\=P(Z<1.96)-P(Z<-1.96)\\=0.975-0.025\\=0.95[/tex]
Thus, the probability that the sample proportion will be within 0.04 of the population proportion is 0.95.
(c)
The sample selected is of size n = 200 > 30.
Then according to the central limit theorem the sampling distribution of sample proportion is normally distributed.
The mean and standard deviation are:
[tex]\mu_{\hat p}=p=0.75\\\\\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.75(1-0.75)}{200}}=0.0306[/tex]
So, the sampling distribution of sample proportion is [tex]\hat p\sim N(0.75,0.0306^{2})[/tex].
(d)
Compute the probability that the sample proportion will be within 0.04 of the population proportion as follows:
[tex]P(p-0.04<\hat p<p+0.04)=P(\frac{-0.04}{0.0306}<\frac{\hat p-p}{\sigma_{\hat p}}<\frac{0.04}{0.0306})[/tex]
[tex]=P(-1.31<Z<196)\\=P(Z<1.31)-P(Z<-1.96)\\=0.9049-0.0951\\=0.8098\\\approx 0.81[/tex]
Thus, the probability that the sample proportion will be within 0.04 of the population proportion is 0.81.
(e)
The probability that the sample proportion will be within 0.04 of the population proportion if the sample size is 450 is 0.95.
And the probability that the sample proportion will be within 0.04 of the population proportion if the sample size is 200 is 0.81.
So, there is a gain in precision on increasing the sample size.
If necessary, combine like terms. (5x+1)(5x-1)
Answer:2 5x^2-1
Step-by-step explanation:
ASAP!!! PLEASE HELP
10 points
An object is moving at a speed of 6 miles per month. Express this speed in feet per hour.
Answer:
44 ft/hr
Step-by-step explanation:
First, we convert miles to feet.
6 mi*5280 = 31680 feet
Now we convert a month to hours. For this question, lets say that a month is equal to 30 days.
30*24 hrs = 720 hrs
Now we have this speed -
31680 ft/720 hrs
Now we simplify this to -
44 ft/hr
So in conclusion, the speed of 6 miles per month is equivalent to the speed of 44 feet per hour.
This table gives a few (x, y) pairs of a line in the coordinate plane. What is the x-intercept of the line?
Answer:
(22,0)
Step-by-step explanation:
22 0
35 -15
48 -30
61 -45
74 -60
2. What is the measure of the missing angle? *
C-120
B-95
A-85
What is D?
Answer:
60
Step-by-step explanation:
it is because 360-(120+85+95)
Y-4>3 solve the question
Answer:
y>7
Step-by-step explanation:
y-4>3
+4 +4
y>7
How do you solve this? Without going into anything to complicated as this should be Year 10 maths
Given : ABCD is a square with each side 5cm .
To Find : The area of the shaded region .
Solution : On observing the figure we can see two quadrants , quadrant ADC & quadrant ABC .
If we join A to C , then it will be common for triangles ADC & ABC . And they will be congruent by SSS congruence condition.
Therefore the area of both quadrants will also be equal . Now we can find area of quadrant as ;
[tex]\large\boxed{\red{\bf Area_{quadrant}=\dfrac{\pi r^2}{4}}}[/tex]
Here radius will be equal to 5cm .
⇒ Area = πr² / 4 .
⇒ Area = π (5cm)² / 4 .
⇒ Area = 22/7 × 25 × 4 cm².
⇒ Area = 19.64 cm² .
So , total area of both quadrants = 39.28 cm² .
Also , area of square will be :
[tex]\large\boxed{\bf{\red{Area_{square}=(side)^2}}}[/tex]
⇒ Area = 5cm × 5cm .
⇒ Area = 25 cm².
Now , subtract area of one quadrant from the area of square = 25cm² - 19.64 cm² = 5.36 cm².
Similarly area of other white region = 5.36cm² .
And the areas sum will be = 5.36cm² × 2 = 10.72cm² .
Now , from the figure it's clear that ,
⇒ Area of unshaded region + Area of shaded region = 25cm².
⇒ 10.72cm² + ar( Shaded region ) = 25cm².
⇒ ar ( Shaded region ) = 25cm² - 10.72cm².
⇒ ar ( Shaded region ) = 14.28 cm².
Hence the area of shaded region is 14.28 cm².
[tex]\large\boxed{\red{\bf Answer = 14.28cm^2}}[/tex]
what is the place value of the 6 in 976.14
Answer:
represents the one value
Step-by-step explanation:
Ones place
Help me please!!..,,
Answer:
A.
Step-by-step explanation:
1.5 x 0.1 = 0.15
0.15 inches
Dont know if this is for sure right. Hope it is.
What decimal is equivalent to StartFraction 8 over 100 EndFraction
Answer:
8/100 is equivalent to 0.08
Which of the following could be the ratio between the lengths of the two legs
of a 30-60-90 triangle?
Check all that apply.
OA. VE2
✓ B. 1: 13
C. 5 : 13
OD. 2.5: 6
E. 1: 2
OF. : 3
Answer:1 squad 3
2 squad 3 :6
Step-by-step explanation:
A scanner can scan 20 pages and 120 seconds. How many pages can scan in 4 minutes?
Answer:
40 pages
Step-by-step explanation:
120 or 2 min x 2 = 4
20 x 2 = 40
Sorry I couldn't explain more, but I hope this helps!
Answer:
40 pages
Step-by-step explanation:
convert 4 mins -> 240 secs
then cross multiply 20/120 and x/240 (x represents the pages scanned)
u then get 120x=4800
simplify(divide)-> x=40
Juan’s cell phone company charges $35 a month for phone service with limited data for every gigabyte of data overage the company charges $15 write an equation that represents how many gigabytes one goes over in a month if his bill was $110
Answer:15x+35=110
Step-by-step explanation:
What’s the value of y in this picture
Answer: A 83
Step-by-step explanation:
Add 46 to 51 then subtract from 180 to get the correct answer(83)
Find the slope of the line y=4x+2
Answer:
M=4
Step-by-step explanation:
I hope this helps!
Ik y’all good at math, help me out yall!
Answer:
i think the answer be 150 feet per minute
hope this is right
Answer:
150
Step-by-step explanation:
use points on the line i'll use (2,300) and (1,150)
m=y2-y1/x2-x1
300-150=150
2-1=1
150/1=150
hope this helps :3
sorry if im wrong
Which equation has the solution x = 9?
Select each correct answer.
+7= 8
4+ 5x = 18
81 – 3 = 6
х
2x – 3 = 15
24 – 2x = 13
3x + 2 = 25
Answer:
2x – 3 = 15
Step-by-step explanation:
2 * 9 = 18 - 3 = 15. correct
+7 = 8, no I don't really now what you mean by this...
81 - 3 = 6x? > (81 - 3 = 78) = (6 * 9 = 54), no, please tell me if I'm interpreting this right.
4 + 5x = 18 > 5 * 9 = 45 + 4 = 49, no
2 * 9 = 18, 24 - 18 = 6, no
3 * 9 = 27 + 2 = 29, no
I know 5his is easy for yall but for me is not I need some help please I'm giving brainlist.
Answer:
$2.99
Step-by-step explanation:
Given parameters:
Selling price = $19.95
Discount percentage = 15%
Unknown:
Amount of discount = ?
Solution:
To find the amount of discount, ;
Discount amount = discount percentage x selling price
Discount amount = [tex]\frac{15}{100}[/tex] x 19.95
Discount amount = $2.99
CHECK PHOTO Intercepts of the graph BE SURE TO BE CORRECT PLEASE no work needed
Answer:
y= (0, .7)
x= (-1.2, 0)
Step-by-step explanation:
r u taking a test?
Determine whether each equation is true or false.
-5/-1 = 5
(0/-4) = 0
-3/1 = -3
- 8/0 = 0
Step-by-step explanation:
1.False
2.True
3.True
4.False
A popular restaurant advertises that it delivers its orders within 30 minutes. Suppose the average delivery time for one store is 27 minutes with a standard deviation of three minutes. One particular order delivery has a z-score of –2.15. Which of the following statements is not a correct interpretation?
A.The delivery time was 2.15 standard deviations below the average delivery time.
B.The delivery time was less than the average delivery time by 2.15 standard deviations.
C.The delivery time was faster than the average delivery time by 2.15 standard deviations.
D.The delivery time was slower than the average delivery time by 2.15 standard deviations.
Answer: B. The delivery time was less than the average delivery time by 2.15 standard deviations.
Step-by-step explanation:
Given: A popular restaurant advertises that it delivers its orders within 30 minutes.
Suppose the average delivery time for one store is 27 minutes with a standard deviation of 3 minutes.
z-score value represents the number of standard deviations is the data value is far from mean.
Here, z-score = -2.15 which clearly indicates that the delivery time was 2.15 standard deviations below( '-' sign suggest value is below mean) the average delivery time.
Hence, the correct option is B.
Answer:
B
Step-by-step explanation:
600 students are studying in a private
school, the average monthly fee of a
student is Rs. 1200. How much amount for
tax does the school pay to the government
as education service tax at the rate of 1% in
a year? *
Answer:
600 ×1200=720,000
720,000×12=8,640,000
8,640,000×1%=8,640,000÷100%=86,400
86,400 per year
Somebody please answer this question I’m begging you
Answer: The answer is A, the y value increases by 1.5 as the x value increases by 1. Therefore A does not describe the graph.
PLZ HURRY IT'S URGENT!!!
What is the slope of the line? y=x−5
options:
undefined
1
0
-5
Answer:
1
Step-by-step explanation:
A mug is 3/7 full. The mug contains 1/2 cup of water. Find the capacity of the mug
Answer:
7/6 cups of water is the mug's capacity
Step-by-step explanation:
Capacity refers to how much a container can contain.
Let x be the capacity of the mug.
According to the question, the mug is 3/7 full. This means that the mug contains 3/7 × x = 3x/7 of water.
It was further stated that the mug contains 1/2cup of water. This means that:
1/2 cup of water = 3x/7 of water in the mug
Hence;
1/2 = 3x/7
3x × 2 = 7 × 1
6x = 7
x = 7/6
Therefore, the capacity of that mug is 7/6 cups of water.
The capacity of the the mug if it is 3/7 full and contains 1/2 cup of water is 7/6 cup
CapacityGiven:
Quantity of the mug = 1/2 cuplet
x = full capacity of the mugWater in the mug = 3/7 of x
= 3/7x
Note:
Water in the mug = 1/2 cup
So,
3/7x = 1/2
divide both sides by 3/7x = 1/2 ÷ 3/7
= 1/2 × 7/3
= 7/6
Therefore, the full capacity of the mug is 7/6 cup
Learn more about fraction:
https://brainly.com/question/2929160
What value of x is in the solution set of 8x -6 > 12 + 2x?
-1
0
3
5
Answer:
x:5
Step-by-step explanation:
The value of 'x' in the solution set is 5 Option D
How to determine the value of xFrom the equation
8x -6 > 12 + 2x
Collect like terms
8x - 2x > 12 + 6
6 x > 18
Make 'x' subject of formula
x > 18/6
x > 3
If x is greater than 3, then x is 5
Therefore, the value of 'x' in the solution set is 5. Option D
Learn more about inequalities here:
https://brainly.com/question/24372553
#SPJ9
A delivery driver earns a fixed amount for each delivery she makes, and
yesterday her average hourly wage was $16.50 an hour. If she worked 6 hours
yesterday and made 11 deliveries, how much does she earn for each delivery
made?
O A. $9.90
O B. $9.00
O C. $5.50
O D. $5.00
Answer:
9 dollars or B
Step-by-step explanation:
16.50 (hourly wage) x 6 (hours worked) = 99 dollars
$99/11 deliveries= 9 dollars per delivery.
Use the drop-down menu to complete the statement.
To find the quotient of 2 -
3
circle groups of
8
loo
Answer:
its 3/8
Step-by-step explanation:
Hopes this helps <3
Mr. Waxman is helping with deliveries for a shipping company. The graph shows a linear model for his delivery times on different days. (A) Identify two points on the line and write the coordinate pairs below. (B) Use your two points to find the slope, and make sure to show your work. (C) Use your slope from Part B and find the equation of the line in point-slope form. Show your work and work through the steps to transform the equation from point-slope form into slope-intercept form. (D) Based on the equation you found in Part C, predict how long it take Mr. Waxman to deliver his packages on Day 0. Approximately how much did his delivery time decrease per day? 2 SEE A
Answer:
See below
Step-by-step explanation:
Note: missing graph is attached
SolutionA) The two points are:
(4, 19) and (7, 7)B) Slope formula: m = (y2-y1)/(x2-x1)
m = (7 - 19)/(7-4)m = -12/3m = -4C) Point-slope formula:
y - y1 = m(x - x1)Using one of the points we get:
y - 19 = -4(x - 4)D) Delivery time on Day 0:
y - 19 = -4(0 - 4)y - 19 = 16y = 16 + 19y = 35 minutesDelivery time decreases by the value of the slope which is 4 minutes per day
Please help with question plaaseeee
Answer:
Yes it is.Step-by-step explanation:
The graph is proportional because
it is in a straight line in the graph.
Hope this helps! <3