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
11. Find the product of (4x-5) and (2x+7) in simplest form.
What’s the unit rate for Tegan?
Answer:
The unit rate is 16
In March it rained 8.23 inches. It rained 5.96 inches less in April than in March.
How much did it rain in April?
Determine the expression
trinomial and i believe its a degree of 4
.
Determine the value of each of the following expressions
a.
25+310
b.
56−13
c.
45×78
d.
67÷34
Help me pleaseeeeeeeeeeeeeeeeee
If the ratio of the length of a rectangle to its width is
9/4 and it’s length is 18 cm, what is the width of the rectangle?
9514 1404 393
Answer:
8 cm
Step-by-step explanation:
It is convenient to write the proportion with the unknown (width) on top:
width/length = 4/9 = w/(18 cm)
Multiplying by 18 cm gives ...
w = (18 cm)(4/9) = 8 cm
The width of the rectangle is 8 cm.
Answer:
The answer is 8.
Step-by-step explanation:
I did a test with this question on it.
This was the correct answer.
YOUR WELCOME!!! HOPE IT WAS HELPFUL :)
it takes Molly 0.25 hours to drive to school. her route is 16 km long. what is Molly's average speed on her drive to school?
Answer:
64
Step-by-step explanation:
16 divided by 0.25 gives you 64 .... welcome
Answer:
64 km/h
I answered it correctly on a mid term
Step 1:Choose the lowest common denominator
Find the sum of 1/5 and 7/10
The expression written in equation from with common denominator is______
The sum is___
Answer:
-6/8 +5/8 and -1/8
Step-by-step explanation:
just got done doing it.
You start an account with $2,500 and an annual interest rate of 6.5% compounded yearly. How much is in the account after 7 years?
I need an expression and a solution
I'm pretty sure it's this:
Answer:
y=a( 1+ r/n)^ nt
growth is a= 2500 yearly is n= 1
y= 2500( 1+ .065/1)^ 1.7 = $3884.97
1. Find the value of k.
A. 17
B. 73
C. 118
D. 107
Answer:
Its B
Step-by-step explanation:
you have to add 45 and 62 to get 107 and then subtract 107 from 180
Hope this helps
pls mark brainliest
#13 Easton is planning on buying a new pair of cowboy boots. When he
went to Eastern Outfitters last week they costs $60 on the black Friday
sale. This week, they aren't on sale anymore and they cost $85. What is the
percent of change on the boots? *
O 25%
O 45%
O 55%
75%
Help i need the answer now please!
Answer:
no
Step-by-step explanation:
-3- 2 1/3 please help me out
Answer:-2/3
-3-2 1/3
which is also
-3 -7/3
which is also
-9/3-7/3
which is
-2/3
I need to know for you to Awnser my question
Points and brainlest !!!
Answer:
id c hot hf hdjhdw fhwjfehf v;e
Step-by-step explanation:
id c h
Answer:
2/3
Step-by-step explanation:
theres only 4 less than 5 out of 6 so the fractio is 4/6. 4/6 simplified is 2/3
13. What is the value of x?
t
(2x +40)
(x +90°
С
D
A. 25
B. 50
C. 75
D. 85
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Answer:
B. 50
Step-by-step explanation:
The alternate interior angles at transversal t across parallel lines AB and CD will be congruent.
2x +40 = x +90
x = 50 . . . . . . . . . . . subtract x+40
The value of x is 50.
_____
Check
2x+40 = 2×50 +40 = 140
x+90 = 50 +90 = 140 . . . . so the obtuse angles are congruent, as they should be
___
Additional comment
The lines AB and CD are not shown as being parallel. We have to assume they are, or we cannot work the problem.
pls solve this and you get the points i'm a lil high right now
Answer:
solve for V= pier^/3
solve for R=Square root3Vpie over pie
Step-by-step explanation:
V=multiply 1/3(pier^2)
R= Take root of both sides and solve
Answer:
dividing by a fraction (1/3) is equivalent to multiplying by its inverse (3)
3+%2A+v+%2F+%28pi+%2A+r%5E2%29 = h
Step-by-step explanation:
The graph of an equation with a negative discriminant always has which characteristic?
OO
no x-intercept
no y-intercept
no maximum
no minimum
18
=
4
Convert the improper fraction to a mixed number.
Answer:
[tex]4\frac{1}{2}[/tex]
Step-by-step explanation:
In order to find the answer to this question you have to divide the numerator by the denominator.
[tex]\frac{18}{4}[/tex]
[tex]4\times4=16[/tex]
[tex]18\div4=4^2[/tex]
[tex]4\frac{2}{4}[/tex]
Reduce:
[tex]2\div2=1[/tex]
[tex]4\div2=2[/tex]
[tex]=4\frac{1}{2}[/tex]
Hope this helps.
a nursery sells kentucky bluegrass seed for $5.75 per pound and tall fescue seed for $4.50 per pound. the nursery sells a mixture of the two kinds of seed for $5.25 per pound. let k represent the amount of kentucky blue grass seed the nusery uses in in 5 pounds of the mixture
Answer:
[tex]k=3[/tex]
Step-by-step explanation:
Given that:
Per pound cost of kentucky bluegrass seed = $5.75
Per pound cost of tall fescue seed = $4.50
Per pound cost of mixture of seeds = $5.25
[tex]k[/tex] is the amount of kentucky blue grass.
Total amount of the mixture = 5 pounds
Therefore, amount of tall fescue seed = (5 - [tex]k[/tex]) pounds
To find:
The value of [tex]k[/tex].
Cost of [tex]k[/tex] pounds of kentucky bluegrass seed = [tex]\$5.75k[/tex]
Cost of (5 - [tex]k[/tex]) pounds of tall fescue seed = [tex]\$(5-k)4.50[/tex]
As per question statement:
[tex]5.75k+(5-k)4.50=5.25\times 5\\\Rightarrow 575k+5\times 450 -450k=525\times5\\\Rightarrow 125k=75\times5\\\Rightarrow k =3\ pounds[/tex]
Amount of kentucky blue grass seed used = 3 pounds
Amount of tall fescue seed used = 5-3 = 2 pounds
Graph the equation y=-x^2+12x-32y on the accompanying set of axes. You must plot 5 points including the roots and the vertex.
The vertex of the quadratic function y = - x² + 12 · x - 32 is located at point (0, - 20) and the roots of the abovementioned are points (4, 0) and (8, 0), respectively.
How to graph a quadratic function
By fundamental algebra theorem we need at least three no coplanar different points to graph quadratic functions. First, we determine 5 different points, then we pass the curve through the five points and finally we identify the roots and the vertex.
If we know that (- 16, - 480), (- 12, - 320), (- 8, - 192), (- 4, - 96), (0, - 32), then the graph of the quadratic function is shown in the image.
The vertex of the quadratic function y = - x² + 12 · x - 32 is located at point (0, - 20) and the roots of the abovementioned are points (4, 0) and (8, 0), respectively.
To learn more on quadratic functions: https://brainly.com/question/5975436
#SPJ2
Lara created a 15-pound platter of three different types of cookies for a banquet. The peanut butter cookies sell for $2 per pound, the sugar cookies sell for $3 and the chocolate chip cookies sell for $3.60 per pound. The entire platter is worth $40. The quantity of peanut butter cookies was 3 more than chocolate chips. How many pounds of each cookie was there. Answered with a chart.
Answer:
i need a bad bleep
Step-by-step explanation:
addison rae
It takes andre 4 minutes to swim 5 laps. At this rate heswims how many laps per minute.
Answer: It takes him 1 minute and 25 seconds
Step-by-step explanation:
5 divided 4
4 times 1 = 4
5-4=1
put the decimal and make 1=10 Ans.: 1.25
4 times 2 = 8
10-8=2
put the 0 = 20
4 times 5 =20
20-20=100
FIRST ONE TO GET ME THE CORRECT ANSWER WILL WIN BRAINIEST
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Answer:
59 3/4
Step-by-step explanation:
The change from the opening price is ...
-50 1/2 +110 1/4 = 60 -1/4 = 59 3/4 . . . change from opening price
Which ordered pair is a solution to the equation below? 3x + 2y = 10
Question 1 options:
(4, 0)
(6, -4)
(-1, 4)
Answer:
(6,-4)
Step-by-step explanation:
I have tried replacing each option with x, y in the equation.
Let's replace (6, -4) with x and y
3x+2y=10
3(6)+2(-4)=10
3(6)= 18 2(-4)= -8
18+(-8)=10
in other words:
18-8=10
The statement is true, so the correct answer is:
(6, -4)
Xavier's car used 4 gallons to travel 152 miles. How many miles can the car go
on one gallon of gas?
Answer:
1 gallon of gas= 38 miles
Step-by-step explanation:
152÷4= 38.
Which equation has the correct sign on the product?
A 45(-4)=180 B 13•3= -39
C (-8)(-8)= -64 D (-18)4 = -72
answer:
the answer is a
The function
The function g(x) has a slope of —5/6. The value of g (x) is 5 when x is 6. Explain how the graph
of g(x) can be used to find the x-intercept. (2 points)
Item
There are 24 female performers in a dance recital. The ratio of men to women is 7:8. How many men are in the dance recital?
what type of angle is 2??
a. Alternate Exterior
b. Alternate Interior
c. Corresponding
d. Linear Pair
e. Same-Side Exterior
f. Same Side Interior
g. Vertical Angles
h. No Relationship
Answer:
Vertical Angles...............