Answer:
a) 0.6212 = 62.12% probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean.
b) 0.7416 = 74.16% probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean.
c) 0.8804 = 88.04% probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean.
d) None of them ensure, that one which comes closer is a sample size of 100 in option c), to guarantee, we need to keep increasing the sample size.
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 establishes 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 CPA Practice Advisor reports that the mean preparation fee for 2017 federal income tax returns was $273. Use this price as the population mean and assume the population standard deviation of preparation fees is $100.
This means that [tex]\mu = 273, \sigma = 100[/tex]
A) What is the probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean?
Sample of 30 means that [tex]n = 30, s = \frac{100}{\sqrt{30}}[/tex]
The probability is the p-value of Z when X = 273 + 16 = 289 subtracted by the p-value of Z when X = 273 - 16 = 257. So
X = 289
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{289 - 273}{\frac{100}{\sqrt{30}}}[/tex]
[tex]Z = 0.88[/tex]
[tex]Z = 0.88[/tex] has a p-value of 0.8106
X = 257
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{257 - 273}{\frac{100}{\sqrt{30}}}[/tex]
[tex]Z = -0.88[/tex]
[tex]Z = -0.88[/tex] has a p-value of 0.1894
0.8106 - 0.1894 = 0.6212
0.6212 = 62.12% probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean.
B) What is the probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean?
Sample of 30 means that [tex]n = 50, s = \frac{100}{\sqrt{50}}[/tex]
X = 289
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{289 - 273}{\frac{100}{\sqrt{50}}}[/tex]
[tex]Z = 1.13[/tex]
[tex]Z = 1.13[/tex] has a p-value of 0.8708
X = 257
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{257 - 273}{\frac{100}{\sqrt{50}}}[/tex]
[tex]Z = -1.13[/tex]
[tex]Z = -1.13[/tex] has a p-value of 0.1292
0.8708 - 0.1292 = 0.7416
0.7416 = 74.16% probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean.
C) What is the probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean?
Sample of 30 means that [tex]n = 100, s = \frac{100}{\sqrt{100}}[/tex]
X = 289
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{289 - 273}{\frac{100}{\sqrt{100}}}[/tex]
[tex]Z = 1.6[/tex]
[tex]Z = 1.6[/tex] has a p-value of 0.9452
X = 257
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{257 - 273}{\frac{100}{\sqrt{100}}}[/tex]
[tex]Z = -1.6[/tex]
[tex]Z = -1.6[/tex] has a p-value of 0.0648
0.9452 - 0.0648 =
0.8804 = 88.04% probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean.
D) Which, if any of the sample sizes in part (a), (b), and (c) would you recommend to ensure at least a .95 probability that the same mean is withing $16 of the population mean?
None of them ensure, that one which comes closer is a sample size of 100 in option c), to guarantee, we need to keep increasing the sample size.
C is actually 0.8904
for anybody else stuck on this wondering why cengage is telling you c is wrong
solve the following ineuality -1+6(-1-3x) >-39-2x
Step-by-step explanation:
(=) 5 (-1-3x) >-39-2x
(=) -5-15x > -39-2x
(=) -13x > -34
=> x < 34/13
An employee makes $11.20 per hour but is getting a 6.5% increase. What is his new wage per hour to the nearest cent? His new wage per hour is?
Answer:
11.93
Step-by-step explanation:
First find the amount of increase
11.20 *6.5%
11.20 *.065
0.728
Rounding to the nearest cent
.73
Add this to the original wage
11.20+.73
11.93
The angle θ between 5i-j+k & 2i-j+k is
Step-by-step explanation:
Let,
[tex] \sf \vec{a} = 5 \hat{i} - \hat{j} + \hat{k} \\ \therefore \: \sf \: | \vec{a}| = \sqrt{ {5}^{2} + {( - 1)}^{2} + {1}^{2} } \\ = \sqrt{25 + 1 + 1} \\ = \sqrt{27} \\ \\ \sf \vec{b} = 2\hat{i} - \hat{j} + \hat{k} \\ \therefore \: \sf \: | \vec{b}| = \sqrt{ {2}^{2} + {( - 1)}^{2} + {1}^{2} } \\ = \sqrt{4 + 1 + 1} \\ = \sqrt{6} \\ \\\sf \: \vec{a}. \vec{b} = (5 \hat{i} - \hat{j} + \hat{k}).(2\hat{i} - \hat{j} + \hat{k}) \\ = 5 \times 2 + ( - 1) \times ( - 1) + 1 \times 1 \\ = 10 + 1 + 1 \\ = 12 \\ \\ \sf \: angle \: between \: \vec{a} \: and \: \vec{b} \: = \theta \\ \\ \: so \\ \sf \vec{a}. \vec{b} = | \vec{a}| . | \vec{b}| cos\theta \\ = > \sf \: cos \theta \: = \frac{ \vec{a}. \vec{b}}{ | \vec{a}| . | \vec{b}| } \\ = > cos \theta = \frac{12}{ \sqrt{27} \times \sqrt{6} } = 0.94 \\ = > \theta = {cos}^{ - 1} (0.94) \\ = > \green{\theta = 19.47 ^{ \circ} }[/tex]
find the derivative of e power ax divide by log bx
Answer:
Step-by-step explanation:
What is the domain of the function in the graph?
Answer:
C
Step-by-step explanation:
You are looking at the domain which is on the K axis. It starts at 6 and ends at 11. The range J is 80 to 120
The correlation between a student’s shoe size and their score on a final exam is −0.79.What conclusions can be drawn based on the correlation coefficient? Select all that apply.
There is a relationship between a student’s shoe size and their final exam score.Big shoe sizes correlate to low exam scores.Large shoe sizes cause students to do poorly on the final exam.As the shoe size decreases, the final exam score increases.Small shoe sizes cause students to do well on the final exam.
(1,2,4) (A,B,D)
Answer:
The first one, the second, and fourth one are correct.
Select A,B, and D.
ED2021
Answer:
A, B, and C
Step-by-step explanation:
I got it right ;)
How is the graph of y=4(2)^x-3 translated from the graph of y=4(2)^x
Subtracting 3 at the end of the equation shifts the graph down 3 units
Help pls and thank you
7+4i+1-3i simplify as much as possible
Answer:
8+i
Step-by-step explanation:
7+4i+1-3i
Combine like terms.
8+i
I hope this helps!
pls ❤ and give brainliest pls
Kylie has a loyalty card good for a 13% discount at her local hardware store. What number should she multiply the prices on the tags by to find the price she would have to pay, before tax, in one step?
Answer:
.87
Step-by-step explanation:
She gets 13 off so 100-13 =87
She will pay 87%
Multiply by .87
Kylie must multiply the price by 0.87 to get the discounted price.
Given that,
Kylie has a loyalty card good for a 13% discount at her local hardware store. What number should she multiply the prices on the tags by to find the price she would have to pay, is to be determined.
The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
let the price be x,
Now,
According to the question,
discounted price = x - 13% of x
Discounted price = x - 0.13x
Discounted price = 0.87 x
The coefficient of the x represents the multiplication factor for Kylie.
Thus, Kylie must multiply the price by 0.87 to get the discounted price.
Learn more about percentages here:
brainly.com/question/13450942
#SPJ2
The pair of figures to the right are similar. The area of one figure is given. Find the area of the other figure to the nearest whole number. Area of larger triangle = 165 ft^2 Thank you!!
9514 1404 393
Answer:
73 ft²
Step-by-step explanation:
The ratio of areas is the square of the ratio of linear dimensions.
smaller area = larger area × ((10 ft)/(15 ft))² = 165 ft² × (4/9)
smaller area = 73 1/3 ft² ≈ 73 ft²
Answer:
Area of the smaller triangle = 73 square feet
Step-by-step explanation:
Area of the larger triangle = 165 square feet
Area of a triangle = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
[tex]\frac{1}{2}(\text{Base})(\text{Height})=165[/tex]
[tex]\frac{1}{2}(15)(\text{Height})=165[/tex]
Height = 22 ft
Since, both the triangles are similar.
By the property of similar triangles,
Corresponding sides of the similar triangles are proportional.
Let the height of smaller triangle = h ft
Therefore, [tex]\frac{h}{22}=\frac{10}{15}[/tex]
h = [tex]\frac{22\times 10}{15}[/tex]
h = 14.67 ft
Area of the smaller triangle = [tex]\frac{1}{2}(10)(14.67)[/tex]
= 73.33
≈ 73 square feet
please help me out with this
Answer:
5<x<29
Step-by-step explanation:
One theorem tells us that if a triangle has two congruent sides and one of the included angle is bigger than the other, the triangle with the included angle that is bigger. has a bigger side than the other.
This is the opposite in this case. The triangles share two sides and we know that the triangle with the side length 18 has a bigger angle than the triangle with the side length 15. So this means that
[tex]48 > 2x - 10[/tex]
Let find the range of x values.
An angle cannot be negative or zero so this means that
[tex]2x - 10 > 0[/tex]
Solve for x.
[tex]2x > 10[/tex]
[tex]x > 5[/tex]
The angle cannot be bigger than 48 so
[tex]48 > 2x - 10[/tex]
Solve for x.
[tex]58 > 2x[/tex]
[tex]29 > x[/tex]
So x must be greater than 5 but less than 29.
True or false? The polynomial 3xy + 4z - 8 is a trinomial.
Answer:
False is the answer.Step-by-step explanation:
answer is False.Answer:
True.
Step-by-step explanation:
A trinomial is an algebraic expression consisting of 3 terms. The terms in this instance are: 3xy, 4z, and -8.
What fraction is equivalent to 0.46464646...
A)
46∕999
B)
46∕99
C)
23∕50
D)
46∕100
Answer:
Hello,
answer is B
Step-by-step explanation:
[tex]0.\overline{46}=\dfrac{46}{99}[/tex]
The answer is a fraction with numerator is the period (46) and the denominator is a number made with 9 as longer that there are digits in the periode (here 2 digits ==> 99)
can anyone heelp me
b
Answer:
B. suggest that you and your boss schedule regular check-ins at lunchtime and at the end of the day
Step-by-step explanation:
It allows you to be ontask at your role (which you are hired for) while at the same time helps your boss know that you are on top of everything. It is the most polite option since you are setting professional boundaries but not complaining and showing frustrations.
(also so that your boss isn't micro-checking on you)
Read the following scenario, which is represented by a polynomial expression. Then answer the questions to interpret the parts of the expression in terms of the given context.
The volunteers at a high school football team’s concession stand are trying to decide on the price of the hot dogs they are selling. When they charge $2 for a hot dog, they sell an average of 70 hot dogs per game. With every $1 increase in the price, the number of hot dogs sold per game decreases by 8.
The volunteers can calculate the revenue earned from selling the hot dogs at each game using the expression -8x2 + 54x + 140, where x is the number of $1 increases in price.
Part A
What is the constant term in the polynomial expression, and what does it represent?
Answer:
x is the number of $1 increase in the price.
If there is no increase, then the total money earned is
2 × 70 = 140
If there is $1 increase, then the total money earned is
(2 + 1) × [70 - 8(1)]
If there is $2 increase, then the total money earned is
(2 + 2) × [70 - 8(2)]
If we continue the pattern, for x times $1 increase, total money earned is
(2 + x)(70 - 8x) = -8x^{2} +54x+140−8x2+54x+140
If we substitute x = 0 in the above equation, we will get
the total money earned = $140.
It means if there is no increase, then the total money earned = 140.
Hence, 140 is the constant term and it represents that there is no increase in price.
Determine the coordinates of the ordered pairs on the coordinate grid.
Answer:
A = (5,7)
B = (0, -1)
C = (-8, -3)
D = (5, -8)
Step-by-step explanation:
Answer:
A = (5, 7)
B = (0, -1)
C = (-8, -3)
D = (5, -8)
To do these problems, trace along in a straight line from the coordinate to the x- axis line and then to the y-axis line. Whatever number you reach will be part of the coordinate.
Hope this helped.
Solve four and two fifths plus two and two thirds
Sabrina is 4 and her brother Sam is 9 years older than she is. In how many years will same be twice as old as Sabrina
Answer:
=4-7
=5
:same will be 5 years older than Sabrina
Choose the number that belongs to the set described
Answer:
Natural numbers,integers, rational numbers, irrational numbers.
Melinda takes out a loan to purchase a car. The balance on her loan after x months is represented by the equation y = 10,000 – 250x and the value of the car after x months is represented by y = 8,000 – 50x. Which statement describes when Melinda’s loan will be equal to the value of the car?
After 10 months, the loan and value of the car will both be equal to $7,500.
After 12 months, the loan and value of the car will both be equal to $7,000.
After 14 months, the loan and value of the car will both be equal to $6,500.
After 16 months, the loan and value of the car will both be equal to $6,000.
Answer:
Step-by-step explanation:
12 months
Answer:
12 months b on edg
Step-by-step explanation:
edg 2022
4 trillion = 4x 10million missing exponent
Answer:
3
Step-by-step explanation:
im pretty sure
Question 19 of 20:
Select the best swer for the question
19. The distance from the center of a round table top to the edge of the table top is 4 ft what is the area of the table top
Answer:
50.26 ft^2
Step-by-step explanation:
Area=pi*r^2
Area=pi*(4)^2=pi*16=50.26
On a recent trip to the convenience Store you picked up 4 gallons of milk 4 bottles of water and 5 snack size bags of chips your total was $28.35 if a bottle of water cost twice as much as a bag of chips and a gallon of milk cost $2.10 more than a bottle of water how much does each item cost
Answer:
The milk cost $2.10 each the snacks cost $1.535 each the water cost $3.07 each
Step-by-step explanation:
I think Im right
Evaluate the equation
9!/6!3!
The population of a town is decreasing exponentially according to the formula
P = 7,285(0.97)t, where t is measured in years from the present date. Find the population in 2 years, 9 months. (Round your answer to the nearest whole number.)
Answer: 6669
Step-by-step explanation:
I hope I did this right... anyways,
t, is represented by years, which is given to us by 2 years and 9 months. Assuming you would put 2.9 for t.
Additionally, as you can't have a decimal for a person, and they've asked for it to be rounded to the nearest whole number, there would be 6669 people in 2 years and 9 months.
The formula used is:
[tex]7285(0.97)^2^.^9[/tex]
A random sample of n1 = 49 measurements from a population with population standard deviation σ1 = 3 had a sample mean of x1 = 9. An independent random sample of n2 = 64 measurements from a second population with population standard deviation σ2 = 4 had a sample mean of x2 = 11. Test the claim that the population means are different. Use level of significance 0.01.
Compute the corresponding sample distribution value. (Test the difference μ1 − μ2. Round your answer to two decimal places.)
Answer:
The answer is "-3.04"
Step-by-step explanation:
[tex]\to \bar{x_1}-\bar{x_2}=9-11=-2[/tex]
Sample distribution:
[tex]z=\frac{\bar{x_1}-\bar{x_2}- \bar{\mu_1}-\bar{\mu_2}}{\sqrt{\frac{\sigma_{1}^2}{n_1}+\frac{\sigma_{2}^2}{n_2}}}\\\\[/tex]
[tex]=\frac{(-2)-0}{\sqrt{\frac{3^2}{49}+\frac{4^2}{64}}}\\\\=\frac{-2}{\sqrt{\frac{9}{49}+\frac{16}{64}}}\\\\=\frac{-2}{\sqrt{\frac{576+784}{3136}}}\\\\=\frac{-2}{\sqrt{\frac{1360}{3136}}}\\\\=\frac{-2}{\sqrt{0.433}}\\\\=\frac{-2}{0.658}\\\\=-3.039\\\\=-3.04[/tex]
Can I have help I am stuck on this problem It would mean the world if u helped me and tysm!! =-)
Answer:
8192
Step-by-step explanation:
2 cells at beginning, so the equation is (2)*(2^(4t)) where t is in hours. At the end of 3 hours, the cells will be 2*(2)^(12)=8192
A random sample of bolts is taken from inventory, and their lengths are measured. The average length in the sample is 5.3 inches with a standard deviation of .2 inches. The sample size was 50. The point estimate for the mean length of all bolts in inventory is
Answer:
[tex]L_x=5.3 inches[/tex]
Step-by-step explanation:
Average length [tex]\=x =5.3 inches[/tex]
Standard deviation [tex]\sigma=0.2 inches[/tex]
Sample size [tex]n=50[/tex]
Generally The point estimate for the mean length of all bolts in inventory is
[tex]L_x= \=x[/tex]
[tex]L_x=5.3 inches[/tex]
PLEASE HELP ASAP, I WILL GIVE BRAINLIEST!
9. What is another name for BD?
10. What is another name for AC?
11. What is another name for ray AÉ?
12. Name all rays with endpoint E.
13. Name two pairs of opposite rays.
14. Name one pair of rays that are not opposite rays.
Answer:
#9. Segment DB
#10 Segment CA
#11. Ray EA
#12. Ray EB, Ray EC, Ray ED, Ray EA
#13 Ray EA & Ray EC
#14. Ray EB and Ray EC
Step-by-step explanation:
For future reference, if you are asked to give another name for a segment, just flip the letters around (same for rays.).
Opposite Rays are rays that share 1 common endpoint, but extend in opposite directions ( together they make a 180 degree angle). Ray EB & EC share an endpoint, but they do not extend in opposite directions.
Hope this helps!
