Answer:
1.31
Step-by-step explanation:
1. If 15% of adults in a certain country work from home, what is the probability that fewer than 42 out of a random sample of 350 adults will work from home? (Round your answer to 3 decimal places)
2. Suppose we want to estimate the proportion of teenagers (aged 13-18) who are lactose intolerant. If we want to estimate this proportion to within 4% at the 95% confidence level, how many randomly selected teenagers must we survey?
Answer:
(1) 0.058
(2) 601
Step-by-step explanation:
(1)
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]
As the sample size is large, i.e. n = 350 > 30, the Central limit theorem can be used to approximate the sampling distribution of sample proportion of adults in a certain country work from home.
Compute the probability that fewer than 42 out of a random sample of 350 adults will work from home:
Sample proportion: [tex]\hat p=\frac{42}{350}=0.12[/tex]
[tex]P(\hat p < 0.12)=P(\frac{\hat p-\mu_{\hat p}}{\sigma_{\hat p}}<\frac{0.12-0.15}{\sqrt{\frac{0.15(1-0.15)}{350}}})\\\\=P(Z<-1.57)\\\\=0.05821\\\\\approx 0.058[/tex]
Thus, the probability that fewer than 42 out of a random sample of 350 adults will work from home is 0.058.
(2)
The (1 - α)% confidence interval for population proportion is:
[tex]CI=\hat p\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
The margin of error for this interval is:
[tex]MOE= z_{\alpha/2}\cdot\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
Given:
MOE = 0.04
Confidence level = 95%
Assume that the sample proportion is 50%.
The critical z-value for 95% confidence level is 1.96.
Compute the required sample size as follows:
[tex]MOE= z_{\alpha/2}\cdot\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
[tex]n=[\frac{z_{\alpha/2}\cdot\sqrt{\hat p(1-\hat p)}}{MOE}]^{2}\\\\=[\frac{1.96\times \sqrt{0.50(1-0.50)}}{0.04}]^{2}\\\\=600.25\\\\\approx 601[/tex]
Thus, the required sample size is 601.
1. Using the normal approximation to the binomial, it is found that there is a 0.05 = 5% probability that fewer than 42 out of a random sample of 350 adults will work from home.
2. Solving the equation for the margin of error of a confidence interval of proportions, it is found that we must survey 601 randomly selected teenagers.
Question 1:
Normal Probability Distribution
In a normal distribution 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]
It 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, which is the percentile of X.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].In this problem:
15% work from home, thus [tex]p = 0.15[/tex].Sample of 350 adults, thus [tex]n = 350[/tex]Then, for the approximation:
[tex]\mu = np = 350(0.15) = 52.5[/tex]
[tex]\sigma = \sqrt{np(1-p)} = \sqrt{350(0.15)(0.85)} = 6.68[/tex]
Using continuity correction, the probability is [tex]P(X < 42 - 0.5) = P(X < 41.5)[/tex], which is the p-value of Z when X = 41.5. So:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{41.5 - 52.5}{6.68}[/tex]
[tex]Z = -1.65[/tex]
[tex]Z = -1.65[/tex] has a p-value of 0.05.
0.05 = 5% probability that fewer than 42 out of a random sample of 350 adults will work from home.
Question 2:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
z is the z-score that has a p-value of [tex]\frac{1+\alpha}{2}[/tex].The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In this problem:
Within 4%, thus [tex]M = 0.04[/tex].We do not have an estimate for the true proportion, thus [tex]\pi = 0.5[/tex].95% confidence level, thus z has a p-value of [tex]\frac{1 + 0.95}{2} = 0.975[/tex], thus z = 1.96.We have to solve for n, then:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.04 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.04\sqrt{n} = 1.96(0.5)[/tex]
[tex]\sqrt{n} = \frac{1.96(0.5)}{0.04}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96(0.5)}{0.04})^2[/tex]
[tex]n = 600.25[/tex]
Rounding up:
We must survey 601 randomly selected teenagers.
A similar problem is given at https://brainly.com/question/24261244
Plzz Due today!
The table below represents a linear function f(x) and the equation represents a function g(x): (See pic)
Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x).
Part B: Which function has a greater y-intercept? Justify your answer.
Answer: The table below represents a linear function f(x) and the equation represents a function g(x): x f(x) −1 -12 0 -6 1 0 g(x) g(x) = 2x + 6 Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x).
PART B: y=mx +b is slope intercept form of linear equation where m=slope and b =y intercept
slope for line for function f(x) =-5-(-1) / -1-0 =-5+1/-1=-4/-1=4
y = 4x+b
3=4(1)+b
3=4+b
-1 =b
y=4x-1
f(x)=4x-1 slope = 4
g(x)=2x -7 slope = 2
b) y intercept for f(x) is -1
and g(x) is -7
so f(x) is having greater y intercept
Terdapat tiga bikar iaitu A, B dan C. Isipadu air didalam bikar C adalah dua
kali ganda isipadu air dalam bikar B. Selepas itu,
[tex] \frac{1}{4} [/tex]
daripada isipadu di dalam
bikar A dituang kedalam bikar B dan baki dituang kedalam bikar C. Isipadu
didalam bikar B dan C seterusnya masing-masing menjadi 400ml dan
1000ml. Apakah isipadu bikar A, B dan C sebelum air di dalam bikar A
dituang ke dalam bikar B dan C.
For the expression: 12 - 7k + 9 - k
What are the terms?
What are the like terms?
What are the coefficients?
What are the constants?
What is the expression simplified?
Answer:
like terms is -7k-k and 12+8
21947÷205 divide and check the result
Answer (3dp):
107.058
Step-by-step explanation:
(image is explanation)
{ vowels in the word ALGEBRA}
Answer:
3 counting ALL VOWELS, or, 2 counting no double ups
Step-by-step explanation:
vowels - a, e, i, o, u
9. The expression x(x-7)+4(x-7) is equivalent to each of the following except which choice?
(1) (x+4)(x-7)
(3) x2-28
(2) x2 – 3x – 28
(4) (x-7)(x+4)
Answer:
I the answer is number 3
x(x-7)+4(x-7)
x²-7x + 4x-28
=x²-3x-28
(x+4)(x-7)
x²-7x+4x-28
=x²-3x-28
(x-7)(x+4)
x²+4x-7x-28
=x²-3x-28
x2 – 3x – 28
the factored form is
=(x+4)(x-7)
The graph displays the distance a CO2 car traveled in a race.
Help!!!
Answer:
5 seconds per foot
Step-by-step explanation:
Answer:A
Step-by-step explanation:
Slope for (20,8)(9,16)?
Answer:
m=-8/11
Step-by-step explanation:
[tex]\frac{Y2-Y1}{X2-X1} =\frac{y}{x}[/tex]
[tex]\frac{16-8}{9-20} =\frac{-8}{11}[/tex]
1+3 pls help me nowwwww
Answer:
4
Step-by-step explanation:
3=1+1+1,
1+1+1+1=4 :p
Please answer this correctly without making mistakes
Answer:
First figure out how many cups are in a gallon. 16 .
Next multiply 16×3= 48
Finally you divide price per cup or 20.16/ 48.
The cost is .42 cents per cup.
Solve the following inequality using both the graphical and algebraic approach:
5-x<2(x - 3) + 5
A) x<2 Graph A
B) x>2 Graph A
C) x<2 Graph B
D) x>2 Graph B
Answer:
a
Step-by-step explanation:
a
The correct answer for the given inequality 5-x<2(x - 3) + 5 is x<2 Graph A
What is an inequality?A relationship between two expressions or values that are not equal to each other is called inequality.
Given that, an inequality 5-x<2(x - 3) + 5
On solving, we get,
5-x < 2x-6+5
5-x < 2x-1
5+1 < 3x
x < 2
Let y₁ = 5-x, and y₂ = 2(x - 3) + 5
Plotting the graph, we get the graph A
Hence, the correct answer for the given inequality 5-x<2(x - 3) + 5 is x<2 Graph A
For more references on inequality, click;
https://brainly.com/question/28823603
#SPJ2
5
Subtract 27 from 43
14
21
Answer:
-0.4522
Step-by-step explanation:
what is y=(-2/3)x+400 as a function?
Answer:
y= −2x/3 + 400
Step-by-step explanation:
Hope this helps :)
Answer: what the other dude said
Step-by-step explanation:
Eighteen cups are equally packed into 6 boxes. Two boxes of cups break. How many cups are unbroken?
Answer:12
Step-by-step explanation:
18/6=3 cups in each box
3*2=6 cups broke=2 boxes
18-6=12 cups are unbroken
Which line has a slope of 0?
Answer:
y= -5
Step-by-step explanation:
Answer:
y= -5
Step-by-step explanation:
Solve the system by substitution or elimination. {y=2x+8y=3x−1 A. (95,585) B. (7, 22) C. (9, 26) D. (75,545)
Answer:
C. (9, 26)
Step-by-step explanation:
By Substitution:
y = 2x + 8
y = 3x - 1
---------------------
2x + 8 = 3x - 1
-x + 8 = -1
-x = -9
x = 9
Now we can choose either of the two equations given to solve for y:
y = 2x + 8
y = 2(9) + 8
y = 18 + 8
y = 26
(9, 26)
By Elimination:
For this process, I am going to rewrite the equation in "x + y" for as it will make it easier to eliminate the variables
y = 2x + 8
2x - y = -8
y = 3x - 1
-3x + y = -1
-----------------
2x - y = -8
-3x + y = -1
-----------------
-x = -9
x = 9
2x - y = -8
2(9) - y = -8
18 - y = -8
-y = -26
y = 26
(9, 26)
Which of these points is closest to the point (7,1)?
Answer:
6,7
Step-by-step explanation:
13,84,85 are the last ones please help
Answer:
49,36,85
Step-by-step explanation:
c in step 4 comes from step 3... 49+36
a and b in step 3 come from step 2... in the same (you've got a - b and then 7 squared - 6 squared, so a is 49 and b is 36
Is [tex]\sqrt{103}[/tex] irrational or rational? What is your reasoning?
Answer: irrational
Step-by-step explanation:
[tex]\sqrt{103}[/tex] is an irrational number because it is not a perfect square. Irrational numbers keep on terminating, so the answer to the question is irrational.
Hope this helps you!
PLEASSSEEE HELPPP ASAPPPPP
Answer:
first one is 32
the second one is 53
Step-by-step explanation:
Answer:
Step-by-step explanation:
Let RS = x , then PS = x²
2x² + 2x = 84
x² + x - 42 = 0
(x + 7)(x - 6) = 0
x = 6
PQ and RS are 6
QR and SP are 36
A length of chain is to be constructed by placing 36 component links end to end. The length of a link produced by a production process is known to be a random variable with a mean of 2.5 cm with a standard deviation 0.2 cm. The 36 links are chosen at random from this process to produce the chain. The mean and standard deviation of the length of chain are, respectively _________.
a. 90 cm, 7.2 cm
b. 36 cm, 1.2 cm
c. 90 cm, 2.7 cm
d. 90 cm, 1.2 cm
e. 36 cm, 7.2 cm
Answer:
d. 90 cm, 1.2 cm
Step-by-step explanation:
Given that:
The sample size n = 36
For the length of the link:
The mean [tex]\overline x[/tex] = 2.5
The standard deviation s = 0.2 cm
In a chosen 36 links, The mean and standard deviation for the length chain is as follows:
Mean = n[tex]\overline x[/tex]
Mean = 36×2.5
Mean = 90 cm
The Standard deviation = s×√n
The Standard deviation = 0.2×√36
The Standard deviation = 0.2×6
The Standard deviation = 1.2 cm
In this graph the y-intercept of the line is (Blank). The equation of the line is y=(Blank) x (Blank) .
Answer:
In the graph, the y-intercept is -2. The equation of the line is [tex] y = x - 2 [/tex]
Step-by-step explanation:
The equation of the line can be written in the slope-intercept form, y = mx + b.
First we need to find:
The slope = m
the y-intercept = b
Using two points on the line, (0, -2) and (2, 0) the slope can be calculated as follows:
[tex] m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 -(-2)}{2 - 0} = \frac{2}{2} = 1 [/tex]
The y-intercept is simply the point at which the line intercepts the y-axis. It is the value of y when x = 0.
Therefore, the y-intercept, b, = -2.
Substitute m = 1 and b = -2 into [tex] y = mx + b [/tex].
Thus, the equation if the line would be:
[tex] y = (1)(x) + (-2) [/tex]
[tex] y = x - 2 [/tex]
Is 319,459 divisible by 2?
yes
no
Submit
Answer:
no
Step-by-step explanation:
319,459 is not an even number
∠7 and angle ______ are supplementary??
a.)∠5 W
b.)∠13 K
Answer:
b angle 13
Step-by-step explanation:
I'm pretty sure
Answer:
a). ∠5
Step-by-step explanation:
both angles ∠7 and ∠5 together add up to 180°
jose trabaja 4 3/4 horas el lunes, 3 1/2 horas el martes, 6 3/4 horas el miercoles, 4 1/2 horas el jueves y 6 horas viernes, y 5 horas el sabado en promedio cuantas horas diarias trabaja
Answer:
5 horas
Step-by-step explanation:
Answer:
Step-by-step explanation:
( [tex]4\frac{3}{4}[/tex] + [tex]3\frac{1}{2}[/tex] + [tex]6\frac{3}{4}[/tex] + [tex]4\frac{1}{2}[/tex] + 6 + 5 ) ÷ 6 =
( 4 + 3 + 6 + 4 + 6 + 5 + [tex]\frac{6}{4}[/tex] + 1 ) ÷ 6 = 30.5 ÷ 6 = [tex]\frac{61}{2}[/tex] × [tex]\frac{1}{6}[/tex] = [tex]\frac{61}{12}[/tex] = [tex]5\frac{1}{12}[/tex] horas al dia
What fraction is larger 3/8 or 10/24?
Answer:
10/24
Step-by-step explanation:
hope this helps :)
Answer:
5/8
Step-by-step explanation:
Have a good day! :)
Factor 15x-10x^3
PLEASE ASNWER ASAP
Answer:
[tex]\huge\boxed{\sf 5x(3-2x^2)}[/tex]
Step-by-step explanation:
[tex]\sf 15x-10x^3\\\\Greatest Common Factor = 5x\\\\So, We'll \ take \ 5x \ common\\\\= 5x ( 3-2x^2)\\\\Thus, this \ is \ the \ factorized\ form\\\\\rule[225]{225}{2}[/tex]
Hope this helped!
~AnonymousHelper1807what is the slope of an equation of the line that passes through the point (3,-5) and has a slope of 0
Answer:
y=0x-5
Step-by-step explanation:
hope this helps :3
if it did pls mark brainliest
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