1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Dmitriy789 [7]
2 years ago
13

The CPA Practice Advisor reports that the mean preparation fee for 2017 federal income tax returns was $273. Use this price as t

he population mean and assume the population standard deviation of preparation fees is $100.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?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?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?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?
Mathematics
1 answer:
skad [1K]2 years ago
6 0

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 \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

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 \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

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 \mu = 273, \sigma = 100

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 n = 30, s = \frac{100}{\sqrt{30}}

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

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{289 - 273}{\frac{100}{\sqrt{30}}}

Z = 0.88

Z = 0.88 has a p-value of 0.8106

X = 257

Z = \frac{X - \mu}{s}

Z = \frac{257 - 273}{\frac{100}{\sqrt{30}}}

Z = -0.88

Z = -0.88 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 n = 50, s = \frac{100}{\sqrt{50}}

X = 289

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{289 - 273}{\frac{100}{\sqrt{50}}}

Z = 1.13

Z = 1.13 has a p-value of 0.8708

X = 257

Z = \frac{X - \mu}{s}

Z = \frac{257 - 273}{\frac{100}{\sqrt{50}}}

Z = -1.13

Z = -1.13 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 n = 100, s = \frac{100}{\sqrt{100}}

X = 289

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{289 - 273}{\frac{100}{\sqrt{100}}}

Z = 1.6

Z = 1.6 has a p-value of 0.9452

X = 257

Z = \frac{X - \mu}{s}

Z = \frac{257 - 273}{\frac{100}{\sqrt{100}}}

Z = -1.6

Z = -1.6 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.

You might be interested in
I need help can somebody answer them with showing me the work thank you :D
Yuki888 [10]

Question 1. It is graph 3 since the y-intercept in the equation is -2 and the y-intercept on the graph 3 is -2. It is also a quadratic function.

Question 2. It is graph two because the equation listed represents a quadratic function that is positive (graph opens up).

Question 3. It is graph 4 since the y-intercept is 2 and the only graph with that intercept is graph 4. Also, the equation represents a linear function.

Hope this helped :))

3 0
3 years ago
A path 2.5m wide is running outside a square field whose side is 45m. Determine the area of the path.
aliya0001 [1]

Answer:

The area of the path would be 231.25 squared meters.

Step-by-step explanation:

Consider the path as 45m (the field's area), then add 2.5m to all of the sides. You'll get 47.5m on all sides. Then you do 47.5² to get 2256.25 squared meters. After that, you'll remove the area of the squared field. To do this, do 45m². By doing this, you'll get 2025 squared meters. Lastly, to finish up the question, do 2256.25 - 2025. This would get you 31.25 squared meters, the answer.

4 0
3 years ago
$69 shoes with a 6% tax
nlexa [21]

6% of 69 is 4.14

So 69 + 4.14 = $73.14

7 0
3 years ago
Read 2 more answers
G = -7 and h = 3 What is the answer for g+h=
andrew11 [14]

Simply plug g and h into the equation:


g + h =


(-7) + (3) = -4

8 0
3 years ago
Read 2 more answers
Plz help i will give brainly!
Irina-Kira [14]

Answer:

The answer is c

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Other questions:
  • Use the diagram. AB is a diameter and AB perpendicular to CD. The figure is not drawn to scale. Which statement is NOT true?
    8·2 answers
  • URGENT! Please help!!Directions are as shown in picture.
    13·1 answer
  • Car X and car Y traveled the same 80-mile route. If car X took 2 hours and car Y traveled at an average speed that was 50 percen
    8·1 answer
  • 8(4k - 4) = -5k - 32
    15·2 answers
  • X f(x) = −x2 + x + 6
    7·2 answers
  • There are 42 students on a large bus and the rest are on a smaller bus. If 40% of the students are on the smaller bus how many t
    5·1 answer
  • 261, 256,251,... what would be the 46th term
    8·1 answer
  • Lin runs 5 laps around a track in 8 minutes.
    10·1 answer
  • Below, the two-way table is given for a
    15·1 answer
  • Someone help asap Ill give brainlest!
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!