a. The probability that the sample proportion will be within ±0.03 of the population proportion is 0.6456.
b. The probability that the sample proportion will be within ±0.03 of the population proportion is 1.985.
What is population proportion?
The probability that a specific event will occur in the population is known as the population proportion. It is a parameter, and the sample proportion statistic is used to estimate it. The percentage of occurrences that occur in the sample is known as the sample proportion.
a. The probability that the sample proportion will be within ±0.03 of the population proportion is P(-0.03 < p - P < 0.003).
We Know that z-score of sample proportion is given by:
z = (p - P)/SE(p), where SE(p) represents standard error.
⇒SE(p) = √(0.3 * 0.7)/200
⇒SE(p) = √0.00105
⇒SE(p) = 0.0324
Now, using the z score, the probability P(-0.03 < p - P < 0.003) is computed as follows:
P(-0.03 < p - P < 0.003) = P(-0.03/SE(p) < p - P/SE(p) < 0.003/SE(p))
= P(-0.03/0.0324 < Z < 0.003/0.0324)
= P(−0.925926 < Z < 0.925926)
= 2P(0 < Z < 0.925926)
P(0 < Z < 0.925926) = 0.3228 (Using standard table)
So,
2P(0 < Z < 0.925926) = 2*0.3228 = 0.6456
Hence, the probability that the sample proportion will be within ±0.03 the population proportion is 0.6456.
b. The probability that the sample proportion will be within ±0.03 of the population proportion is P(-0.08 < p - P < 0.008).
Also, SE(p) = 0.0324
Now, using z score,
P(-0.08 < p - P < 0.008) = P(-0.08/SE(p) < p - P/SE(p) < 0.008/SE(p))
= P(-0.08/0.0324 < Z < 0.008/0.0324)
= P(−2.469135 < Z < 2.469135)
= 2P(0 < Z < 2.469135)
P(0 < Z < 2.469135) = 0.9925 (Using standard table)
So,
2P(0 < Z < 2.469135) = 2*0.9925 = 1.985
Hence, the probability that the sample proportion will be within ±0.03 of the population proportion is 1.985.
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an anthill has a volume of 8792mm^3 of dirt. its radius is 20 mm. what is the height of the cone? explain how you found the height.
Answer:
Height, h = 21 millimeters.
Step-by-step explanation:
Given the following data;
Volume = 8792mm³
Radius = 20 mm
To find the height;
We know that the shape of an anthill is conical in nature.
Mathematically, the volume of a cone is given by the formula;
[tex] V = \frac{1}{3} \pi r^{2}h[/tex]
Where;
V is the volume of the cone.r is the radius of the base of the cone.h is the height of the cone.Substituting into the equation, we have;
[tex] 8792 = \frac{1}{3} * 3.142*20^{2}*h [/tex]
[tex] 8792 = \frac{1}{3} * 3.142*400*h [/tex]
[tex] 8792 = \frac{1}{3} * 1256.8*h [/tex]
[tex] 8792 = 418.93*h [/tex]
[tex] Height, h = \frac {8792}{418.93}[/tex]
Height, h = 20.99 ≈ 21 mm.
Therefore, the height of the cone is 21 millimeters.
Someone Please Help I Need the awnser
Answer:
x=53
Step-by-step explanation:
2x-24=82(alt.ext.∠)
2x=106
x=53
Shade 12 squares on the 4-by-10 grid.
What percent to is shaded?
On a 10 by 4 grid, there would be 40 squares. If you were to shade 12 of those squares, it can be shown as the fraction:
[tex]\frac{12}{40}[/tex]
12/40 = 0.3
to get a percentage, we would have to multiply by 100
30% is to be shaded
Answer: 30%
Step-by-step explanation:
Total number of squares: 4*10=40
Shaded squares: 12
Fraction of shaded squares: 12/40
If you make the denominator 100, then the numerator is the percentage:
[tex]\frac{12}{40} * \frac{2.5}{2.5}=\frac{30}{100}[/tex]
−3xy ^5 (8y) Simplified
A line is represented by the equation y = 3x – 7. Which statement about the line is TRUE?
A.
This line is parallel to the line whose equation is y = 2x – 7.
B.
The line has a positive slope.
C.
The y-intercept is 7.
D.
The point (1, 4) lies on the line.
Step-by-step explanation:
alignment in represented by erosion by which a statement both lights it's true that this line is a parallel that two parallel whose the equation is do you audio will be that a googlmy answer if two line was station then represented by equation allowed is a representation equation the by represented is a
what is the value of 4 in 204?
Step-by-step explanation:
its on one's place
204 = 2× 100 + 4× 1
4 = 4 × 1
Medians and IQRs. For each part, compare distributions (1) and (2) based on their medians and IQRs. You do not need to calculate these statistics; simply state how the medians and IQRs compare. Make sure to explain your reasoning. (a) (1) 3, 5, 6, 7, 9 (2) 3, 5, 6, 7, 20 (b) (1) 3, 5, 6, 7, 9 (2) 3, 5, 7, 8, 9 (c) (1) 1, 2, 3, 4, 5 (2) 6, 7, 8, 9, 10 (d) (1) 0, 10, 50, 60, 100 (2) 0, 100, 500, 600, 1000
For each part, compare distributions (1) and (2) based on their medians and IQRs. The reasoning is explained is given.
What is median?The median is the value that splits the mathematical numbers or expressions in the half. The median value is the middle number of data point. To find the median, firstly arrange the data points in ascending order.
The middle number in the distribution of the provided data is known as the median. The range of values in the center of the scores is known as the interquartile range, or IQR.
(a). (1) 3, 5, 6, 7, 9 (2) 3, 5, 6, 7, 20
Since all the values are identical except the highest, the distributions' median and IQR will be equal.
(b). (1) 3, 5, 6, 7, 9 (2) 3, 5, 7, 8, 9
The median is higher for the second distribution because in the case of (2) the middle number is larger.
Since the final few digits in the second distribution are higher, the IQR would be wider for the second distribution, resulting in a greater third quartile for the second distribution than the first distribution.
(c). (1) 1, 2, 3, 4, 5 (2) 6, 7, 8, 9, 10
Given that every number in the second distribution is greater than every other number in the first distribution, the median of the second distribution is higher than that of the first distribution.
Since there are the same number of items in both distributions and each number in both distributions is 1 larger than the preceding number, the IQR of both distributions would be identical.
(d). (1) 0, 10, 50, 60, 100 (2) 0, 100, 500, 600, 1000
Since all the values in the second distribution are higher than those in the first in this situation, the second distribution will have a higher median. Given that the spread of the numbers is wider in the second distribution than it is in the first, the second distribution will likewise have a higher IQR.
Therefore, the reasoning is explained.
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My 11 year old sister needs help.
Answer:
1¼ pounds
or 1.25 pounds
Step-by-step explanation:
The lightest bunch = ⅛*5 = ⅝
The heaviest bunch = 1(⅛*+7) = 1⁷/8
Find the difference between the heaviest and the lightest bunch
1⅞ - ⅝
= 15/8 - 5/8
= (15 - 5)/8
= 10/8
= 5/4
= 1¼ pounds
or 1.25 pounds
A tree casts a shadow 38 m long.
At the same time, the shadow cast by a 37 cm tall
statue is 75 cm long.
Find the height of the tree. Use correct units.
Answer:
Step-by-step explanation:
let the height of tree=h
[tex]\frac{h}{38} =\frac{37}{75} \\h=\frac{37}{75} \times 38 \approx 18.75 ~cm[/tex]
Lilly, Madelyn, Natalie, and Olivia each walked from their houses to the mall. Lilly walked 1/4 mile, Madelyn walked 3/8 mile, Natalie walked 5/6 mile, and Olivia walked 7/12 mile. what is the order of these distanced from least to greatest?
Answer:
1/4, 3/8, 7/12, 5/6
Step-by-step explanation:
First, change all the fractions so they have the same denominators. The least common denominator is 24. 1/4=6/24 3/8=9/24 5/6=20/24 7/12=14/24
Now, put them in order from least to greatest: 6/24, 9/24, 14/24, 20/24
emeril is building a cutting board for his home kitchen.He wants it to be similar in size to the cutting board at gis restaurant.His restaurant cutting board is 36 inches wide by 21 inches long .He has enough space on his home counter for a board that is 24 inches wide.How long will his home cutting board be?
Answer:
14 inches
Step-by-step explanation:
I say 14 inches because width for the board at the restaurant is 36 (3×12) and the length is (3×7) so if the width for the board at home is 24 ( 2×12) then the length must be 14 ( 2×7). See what I did?
His home cutting board will be 14 inches long.
Since Emeril is building a cutting board for his home kitchen, and he wants it to be similar in size to the cutting board at gis restaurant, which is 36 inches wide by 21 inches long, and he has enough space on his home counter for a board that is 24 inches wide, to determine how long will his home cutting board be the following cross multiplication calculation must be performed:
36 = 24 21 = X (21 x 24) / 36 = X 14 = X
Therefore, his home cutting board will be 14 inches long.
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Jessie stacked photographs of 6 zoo animals on top of each other to create a display. Each photo is 14 1/4 in. high. How high is the display?
Answer:
85 1/2 inches
Step-by-step explanation:
14 1/4 x 6 = 85 1/2 inches
Hope that helps!
Si un jarrón tíene 80 cm de altura ¿ cuantos milímetros mida
Si tiene 80 cm de altura mier 800 milímetros de altura
The latest online craze is a new game, Khan on Seven. You get 100 points for playing the game. In addition, you
get 50 points for each seven-letter word you make with the ten letters you receive. Sal wants to break the
record, and he needs 18,000 or more points to do so.
Write an inequality to determine the number of seven-letter words, w, Sal could make to break the record.
Graph the solution set to this inequality.
+
352
350
354
356
358
360
362
364
Switch direction
Make circle open
He needs 18,000 points.
He starts with 100, so subtract the 100 from 18,000 to get how many more points he needs:
18000 - 100 = 17,900 more points.
Divide the points needed by points per word:
17,900 / 50 = 358
He needs at least 358 words.
The inequality would be 50x+100>=18000, where x is the number of words.
Because 358 can be part of the solution, a solid dot on 358 and the line/arrow needs to point to the right for greater than.
1. (-13.8) and (3, 12)
Hello!
What do you need me to solve?
A person has 10 Rap songs, 12 R&B songs, 23 Alternative songs, 10 Pop songs, 17 Country songs, and 18 Hip Hop songs stored on an MP3 player (a total of 90 songs). If the person set the MP3 player to random shuffle, what are the probabilities of the first song being played being a Country song?
A) .4888
B) .3888
C) .2888
D) .1888
-1/4(d+1)<2
HELP ME PLEASE
Answer: u suck at math just dont do it duh
Step-by-step explanation: its five
Anybody know how to do this??
Answer:
Second option: x= (23.5)(1.18)
Step-by-step explanation:
It has the total and the 1 for the tip to include the original price.
Answer:
option 2:- x= (23.5)(1.18)
Step-by-step explanation:
it includes the whole amount plus the tip to be paid after dinner..
please help aaa last Q cries
Answer:
C
Step-by-step explanation:
Hope it helps!
Answer:
Answer C is correct
Step-by-step explanation:
The left side equals 1/25, but the righ side is 625
(I usually give a better explanation, but i'm in a bit of a rush. sorry!)
Solve: 3/7 * 6/11 * 2/3. Simplify if possible. Leave answer in improper format.
Answer:
Exact Form:
12 /77
Decimal Form:
0. 155844
Step-by-step explanation:
(a) At Smith's Bike Rentals, it costs $18 to rent a bike for 4 hours.
How many dollars does it cost per hour of bike use?
Answer:My answer is $4.50 a hr. If u add 4.50 up 4 times, you will get 18. If u multiply 4.50 ×4 it will equal 18.
Step-by-step explanation:
A bag of garden soil weighs 38 pounds and holds 4 cubic feet. Find the weight of 15 bags in kilograms and the volume of 15 bags in cubic yards.
Answer:
The weight of 15 bags is 258.21 kilograms.
The volume of 15 bags is 2.222 cubic yards.
Step-by-step explanation:
Dimensionally speaking, a pound equals 0.453 kilograms and a cubic yard equals 27 cubic feet. We proceed to calculate the weight and the volume of 15 bags by following conversions:
Weight
[tex]x = 15\,bags \times \frac{38\,lb}{1\,bag}\times \frac{0.453\,kg}{1\,lb}[/tex]
[tex]x = 258.21\,kg[/tex]
The weight of 15 bags is 258.21 kilograms.
Volume
[tex]x = 15\,bags \times \frac{4\,ft^{3}}{1\,bag} \times \frac{1\,yd^{3}}{27\,ft^{3}}[/tex]
[tex]x = 2.222\,yd^{3}[/tex]
The volume of 15 bags is 2.222 cubic yards.
3m+n=10
5m-2n=2
what is the answer for this one
Answer:
m = 2
n = 4
Step-by-step explanation:
Ok so to solve this, you want to get it so there is only one variable and then solve that equation. To do this, you can start by doing:
3m + n = 10
multiply both sides by 2
6m + 2n = 20
now, in both of your equations you have 2n so you can add the two equations:
6m + 2n = 20
+ 5m - 2n = 2
11m = 22
divide both sides by 11
m = 2.
Now, plug this value into the original equation, 3m + n = 10:
3 * 2 + n = 10
6 + n = 10
subtract 6 from both sides
n = 4
Anna and josh are putting up lights for a party. For every 4 blue lights they put up 2 red lights. If they put up 120 lights. How many are blue?
Answer:
80 blue
Step-by-step explanation:
r=red
b=blue
4b+2r=6 lights in one light cluster
120/6=20 clusters
20 clusters of 4 blue lights =80
A salesperson works 40 hours per week at a job where she has two options for being paid. Option A is an hourly wage of 23$. Option B is a commission rate of 4% on weekly sales. How much does she need to sell this week to earn the same amount with the two options?
Answer:
maybe 17% as u look at the question u will understand
determine the amount of an investment if $500 is invested at an interest rate of 4.25% compounded quarterly for 12 years
someone help me with number 8
Answer:
The answers are...:
The common ratio is -3
the sequence of the function is 2,-6, 18, -54, 162
and
the sequence of the function model is geometric
I hope this helps ^^"
Step-by-step explanation:
the common ratio is just from the -3 itself
the sequence model is just plugging n for every term so
a(1) would equal to 2, a(2)=-6 , a(3) would equal to -18, etc
and the geometric is bc it has the exponential that has (n-1), thus it is a geometric sequence
Simplify: 7^6 divided 7^2
Answer:
The answer is 1/3
Step-by-step explanation:
Reduce the expression, if possible, by cancelling the common factors.
~Hoped this helped~
which expression represents the product of 83 and x
83+x
83÷x
83x
83-x
y + 51 = 99, what is y?
Answer:
y + 51=99
replace the y with 99
then it becomes 99 - 51
y=48