Answer:
0.5934 = 59.34% probability that a sample of 100 taxpayers from this income group who have itemized deductions will show a sample mean within $200 of the population mean.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set 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]
The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The mean amount of deductions for this population of taxpayers as $16642. The standard deviation was of $2400.
This means that [tex]\mu = 16642, \sigma = 2400[/tex]
Sample of 100:
This means that [tex]n = 100, s = \frac{2400}{\sqrt{100}} = 240[/tex]
What is the probability that a sample of 100 taxpayers from this income group who have itemized deductions will show a sample mean within $200 of the population mean?
This is the pvalue of Z when X = 16642 + 200 = 16842 subtracted by the pvalue of Z when X = 16642 - 200 = 16442. So
X = 16842
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{16842 - 16642}{240}[/tex]
[tex]Z = 0.83[/tex]
[tex]Z = 0.83[/tex] has a pvalue of 0.7967
X = 16442
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{16442 - 16642}{240}[/tex]
[tex]Z = -0.83[/tex]
[tex]Z = -0.83[/tex] has a pvalue of 0.2033
0.7967 - 0.2033 = 0.5934
0.5934 = 59.34% probability that a sample of 100 taxpayers from this income group who have itemized deductions will show a sample mean within $200 of the population mean.
Solve for x. 20x + 5 =5x+65
Answer:
x = 4
Step-by-step explanation:
subtract 5 from all sides
20x+5-5=5x+65-5
simplify
20x=5x+60
subtract 5x from both sides
20x-5x=5x+60-5x
simplify again
15x=60
Divide both sides by 15
15x/5 = 60/15
lastly simplify to get your answer of
x = 4
2 1/2 c + 6 1/2 = 19
C = ?
Answer:
C=5
Step-by-step explanation:
5/2c+13/2=19
5/2c=25/2
c=5
The state of New Mexico is piloting a new program that the governor hopes will increase the proportion of people who regularly go for medical check-ups. Historicallty, this rate was known to be 76%. To help them answer this question, they conduct a study that samples 880 people who live in New Mexico. All of these people participate in the pilot program for 6 months. After participation, they are asked whether the now regularly go for medical check-ups. Of the participants, 686 now say they now regularly go for medical check-ups. Consider the scenario in which this program is rolled out state-wide.
Required:
Formulate the null and alternative hypotheses for what would happen in the whole state based on the data observed in the sample. The null hypothesis H 0 stated in words is tha
Answer:
H0: p1=p2 against the claim Ha: p1≠p2
Step-by-step explanation:
Here the proportion of the people going for medical checkup before the program is p1= 0.76
The proportion of the people going for medical checkup after the program is p2= 686/880=0.78
Our null and alternate hypothesis will be
H0: proportion of the people going for medical checkup before the program is equal to the proportion of the people going for medical checkup after the program
against the claim
Ha: proportion of the people going for medical checkup before the program is not equal to the proportion of the people going for medical checkup after the program
Mathematically this can be written as
H0: p1=p2 against the claim Ha: p1≠p2
THE TOPIC IS: AREA OF CIRCLES!! PLEASE HELP ME WITH THIS QUESTION!!! WHATS THE ANSWER?? I WILL GIVE YOU BRAINLIEST AND A THANKS!!! AND PLS PUT AN EXPLANATION!! THANK YOUU
Answer:
49pi, or 153.93
Step-by-step explanation:
pi*r^2=Area
14/2=7=r
r^2=7^2=49
Answer:49pi or 153.93
Plz give brainliest as you said you would!
If f(x) = k(x - 2)^2, where k is positive, what is the effect on the graph of f(x) as k increases
Answer:
The value of k determines where the parabola is on the y-axis. In other words, its "height". If k we're to be positive, the parabola would move to the positive side of y-axis, not negative.
3/4 + 1/2 times 2 please help thanks
Answer:
7/4
Step-by-step explanation:
1/2 x 2 = 1
3/4 + 1 = 7/4 or 1 3/4
A 20-minute consumer survey that included a $5 Starbucks gift card was emailed to 500 adults aged 25-34. The survey resulted in 65 responses. The same 20-minute consumer survey was emailed to 500 adults aged 25-34 without the Starbucks gift card. The survey resulted in 45 responses. We would like to know if the inclusion of a Starbucks gift card led to any change in survey response rate. Which of the following hypotheses should be used?
A. Null Hypothesis: mul (average number of responses with Starbucks gift card)<= muo(average number of responses without Starbucks gift card) Alternative Hypothesis: mu1 ( average number of responses with Starbucks gift card)> muo(average number of responses without Starbucks gift card)
B. Null Hypothesis: mu1 (average number of responses with Starbucks gift card)= mud (average number of responses without Starbucks gift card) Alternative Hypothesis: mu1 ( average number of responses with Starbucks gift card) \= mul ( average number of responses without Starbucks gift card) * \= means "not equal to"
C. Null Hypothesis: pi1 (rate with Starbucks gift card)= pi2 (rate without Starbucks gift card) Alternative Hypothesis: pi1 (rate with Starbucks gift card) (= pi2 (rate without Starbucks gift card) * \= means "not equal to"
D. Null Hypothesis: pi1 (rate with Starbucks gift card) - pi2 (rate without Starbucks gift card)<=0 Alternative Hypothesis: pi1 (rate with Starbucks gift card) - pi2 (rate without Starbucks gift card) > 0
Answer:
D. Null Hypothesis: pi1 (rate with Starbucks gift card) - pi2 (rate without Starbucks gift card)<=0 Alternative Hypothesis: pi1 (rate with Starbucks gift card) - pi2 (rate without Starbucks gift card) > 0
Step-by-step explanation:
The test described above test the difference in proportion :
With Starbucks gift card :
x1 = 65 n1 = 500
Phat 1 = x1 / n1
Phat 1 = 65 /500 = 0.13
Phat1
Without Starbucks gift card :
x2 = 45 n2 = 500
Phat1 = x2 / n2
Phat 2 = 45 / 500 = 0.09
To test the difference in proportion :
Phat 1 > Phat 2 (alternative)
Null takes the stance that there is no difference in proportion
Phat1 - phat2 <=0
Alternative claims that there is difference on proportion such that phat 1 is greater than phat 2
Phat 1 - phat > 0
Please answer no links or repo and no random stuff thanks. no robots please.
Answer: D Maybe?????
Step-by-step explanation:
9xy^2 when x= -2/3 and y =3/4?
Answer: -27/8
Step-by-step explanation:
9 (-2/3)(3/4)^2
(-18/3)(9/16)
(-6)(9/16)
-(6*9)/16
-54/16
-27/8
Domain and Range?? explain pls
Answer:
Dominan is X.
Range is Y
Step-by-step explanation:
Answer:
Range is Y and Domain is x
Step-by-step explanation:
CAN SOMEONE PLEASE HELP ME WITH THIS, TELL ME THE ANSWER AND HOW YOU GOT IT
Answer:
make a net making a net is quite simple
Step-by-step explanation:
you make it by making all sides 2 d then putting lengths next to those sides
for better reference look up how to make a net math videos section also give me a thanks please
I actually need help fast please!!
Answer:
D. The new graph is steeper than the parent function and the y-intercept is translated 2 units down.
Step-by-step explanation:
The -2 means down 2 units.
The 4 means the function is multiplied by a factor of 4.
The length of a rectangle is 8 inches more than the width. The perimeter is 36 inches. Find the length and the width (in inches).
Answer:
width= 5 inches
length= 13 inches
Step-by-step explanation:
width= W
length= w+8
perimeter= 2(lengths)+ 2(width)
(subsistute is known values)
multiply
36=2(w+8) 2(W)
add
36=4W
Divide both sides by 4
W=5
Length=5+8 inches= 13
the item is $21 and has a 30% increase. what is the amount of increase
Answer:
21 multiplyed by .3%
Step-by-step explanation:
Chicago has a population of about 2,715,000. Its territory can be modeled as a parallelogram, as shown in the figure. Each unit on the coordinate grid represents one mile. Find the approximate population density of Chicago. Round to the nearest hundred if necessary.
The population density is approximately _______ persons/mi2
.
Answer:
What was the answer?
Step-by-step explanation:
Answer:
It’s 13,575 persons/mile square
Step-by-step explanation:
Area= bh= (10)(20)=200
2715000/200=13575
Please help me with this assignment
Thank You!
Answer:
then use the selling price formula
100+profit/100×cp
(100+60/100)×400
this is how u will get your answer
BTW can mark me brainliest I need it
and if u still can't understand tell me
I hope I am correct if wrong place correct me
please help ill give extra points
Answer:
Step-by-step explanation:
i think it would be c
What is the length of EF?
Answer:
4n
Step-by-step explanation:
Two numbers are missing from this table. How can the missing numbers be found.
which operation is represented by 4x
algebraic expressions
Measurement of a circle
(Giving brainliest to correct answer)
Answer:
C. [tex] 9\pi [/tex]
Step-by-step explanation:
VU is tangent [tex] \odot W[/tex] at point U and WU is radius.
[tex] \therefore WU \perp VU[/tex]
[tex] \implies m\angle VUW=90\degree[/tex]
[tex] \therefore \triangle VUW[/tex] is right angle triangle.
WZ = WU = x - 1 (Radii of same circle)
WV = x - 1 + 2 = x + 1
By Pythagoras Theorem:
[tex] WU^2 + VU^2 = WV^2 [/tex]
[tex] (x-1)^2 +(2x-4) ^2 = (x+1)^2 [/tex]
[tex]x^2 -2x +1+ 4x^2 -16x + 16=x^2 +2x +1[/tex]
[tex]4x^2 -20x + 16=0[/tex]
[tex]x^2 -5x + 4=0[/tex]
[tex]x^2 -5x + 4=0[/tex]
Equating it with
[tex]ax^2 +bx +c=0[/tex]
We find:
a = 1, b = - 5, c = 4
[tex] b^2 - 4ac =(-5)^2 - 4(1)(4)= 25-16 =9[/tex]
[tex] x=\frac{-b\pm \sqrt{b^2 - 4ac}}{2a} [/tex]
[tex] x=\frac{-(-5)\pm \sqrt{9}}{2\times 1} [/tex]
[tex] x=\frac{5\pm 3}{2} [/tex]
[tex] x=\frac{5+3}{2}, \: x =\frac{5-3}{2} [/tex]
[tex] x=\frac{8}{2}, \: x =\frac{2}{2} [/tex]
[tex] x=4, \: x =1 [/tex]
When x = 4, radius (r) = 4 - 1 = 3
When x = 1, radius (r) = 1 - 1 = 0, which is not possible.
Area of [tex] \odot W [/tex]
[tex] =\pi r^2 [/tex]
[tex] =\pi (3)^2 [/tex]
[tex] =9\pi [/tex]
Use your equation to predict the value of U.S. Computer and Video Game Unit Sales in 2018. ŷ = -1.93273X + 228.56727
Answer:
-3,671.68187
Step-by-step explanation:
-1.93273(2018) + 228.56727 = -3671.68187
Answer:
Write a linear model in slope-intercept form, then substitute 18 for x and solve for y.
Step-by-step explanation:
Who graph shows a rate of 60 feet per second?
Answer:
g i did that before
Step-by-step explanation:
sam earns a salary of $25000, while charlie earns a salary of $30000
Answer:
5000 difference
Step-by-step explanation:
Which of these sums is greater than 1?
A. 12+23
B. 13+18
C. 14+25
D. 15+110
Answer:
b
Step-by-step explanation:
I just know it's greater than 1
Answer:
all of them
Step-by-step explanation:
12 + 23 = 35
35 is greater than 1
13 + 18 = 31
31 is greater than 1
14 + 25 =39
39 is greater than 1
15 + 110 = 125
125 is greater than 1
The situation that will help reduce frictional force. A. tearing of bike gears B. applying lubricants to tires C. rubbing together two hard objects D. sliding big boxes on the ramp from the truck
Please answer my question I need it tommorow...
1/8 plus 3/4: lolz tell me u need help
Answer:
0.875
Step-by-step explanation:
Answer:
7/8
Step-by-step explanation:
1/8 = 1/8
3/4 = 6/8
1/8 + 6/8 = 7/8
The answer should be 7/8.
Helppppppppppppppppp
Answer:
7
Step-by-step explanation:
19-2-3=14
14=2w
W=7
a sale girl receive a 5% commission on all she self. how much she has to sell to receive $15
Answer:
$300
Step-by-step explanation:
Sales x .05 commission = $15
sales=$15/.05
sales = 300
Please answer number 11 I’ll give brainliest thank you!
Answer:
x=28 cm
Step-by-step explanation:
Ratio of length of bigger sides to smaller sides=20:10=2:1.
[tex]\frac{x}{14}=\frac{2}{1}[/tex]
[tex]x=28[/tex]