QSO

QSO 510: Module 2 Homework
Notes:

Before doing this assignment, do the practice problem posted under Apply and Discover.
Word-process your solutions within this template. Do not create a new file.
Show all steps used in arriving at the final answers. Incomplete solutions will receive partial credit.
Word-process formulas using Equation Editor and diagrams using Drawing Tool.

Problem 1
If many samples of size 15 (that is, each sample consists of 15 items) were taken from a large normal population with a mean of 18 and a variance of 5, what would be the mean, variance, standard deviation, and shape of the distribution of sample means? Give reasons for your answers. Note: Variance is the square of the standard deviation. Adapted from Statistics for Management and Economics by Watson, Billingsley, Croft, and Huntsberger. Fifth Edition. Chapter 7 Page 308. Allyn and Bacon. 1993x = 18  2x=5 shape = normal
Therefore x= 2x = 5 = 2.2360
If a large number of samples, each of size 15, are selected from the population and a sample mean is selected computed for each sample, the mean, variance, and shape of the distribution of sample means would be as follows: x= 18. The standard deviation of the sample means x can be computed as given below: x = X = 2.2360 = 0.5773 n 15.  Variance is the square of the standard deviation. Therefore, the variance of the sample means ²x can be computed as follows:
²x = ²x = 5 = 0.3333 n 15.
The shape of the distribution of sample means = normal since sample size n 30.
Problem 2
If many samples of size 100 (that is, each sample consists of 100 items) were taken from a large non-normal population with a mean of 10 and a variance of 16, what would be the mean, variance, standard deviation, and shape of the distribution of sample means? Give reasons for your answers. Note: Variance is the square of the standard deviation. Adapted from Statistics for Management and Economics by Watson, Billingsley, Croft, and Huntsberger. Fifth Edition. Chapter 7 Page 308. Allyn and Bacon.
1993 x = 10 2x=16 shape =non- normal
Therefore x= 2x = 16 = 4.
If a large number of samples, each of size 100, are selected from the population and a sample mean is selected computed for each sample, the mean, variance, and shape of the distribution of sample means would be as follows: x= 10
The standard deviation of sample means x can be computed as given below:
x = X = 4 = 0.4 n 100.
Variance is the square of the standard deviation. Therefore, the variance of the sample means ?²x? can be computed as follows:
²x = ²x = 16 = 0.16 n 100.
The shape of the distribution of sample means = normal since sample size n 30.
Problem 3
Time lost due to employee absenteeism is an important problem for many companies. The human resources department of Western Electronics has studied the distribution of time lost due to absenteeism by individual employees. During a one-year period, the department found a mean of 21 days and a standard deviation of 10 days based on data for all the employees.

a) If you pick an employee at random, what is the probability that the number of absences for this one employee would exceed 25 days?
b) If many samples of 36 employees each are taken and sample means computed, distribution of sample means would result. What would be the mean, standard deviation, and shape of the distribution of sample means for samples of size 36? Give reasons for your answers.
c) A group of 36 employees is selected at random to participate in a program that allows a flexible work schedule, which the human resources department hopes will decrease employee absenteeism in the future. What is the probability that the mean for the sample of 36 employees randomly selected for the study would exceed 25 days?

Source: Statistics for Management and Economics by Watson, Billingsley, Croft and Huntsberger. Chapter 7 Page 305. Fifth Edition. Allyn and Bacon 1993.

a) For x = 25, z = 25-21/10 = 0.4 From the z table p (0 < z < .4) = .1554

Therefore, p (x > .4) = .5 – p(0 < z < .4) = .5 – .1554 = .3446 = 34.46%

b) x = 21 x=10
If a large number of samples, each of size 36, are selected from the population and a sample mean is selected computed for each sample, the mean, variance and shape of the distribution of sample means would be as follows: x= 21.

The standard deviation of sample means x can be computed as given below:
x = X = 10 = 1.6666 n 36.
Variance is the square of the standard deviation. Therefore, the variance of the sample means ²x can be computed as follows:
²x = ²x = 10² = 2.7777 n 36.
The shape of the distribution of sample means = normal since sample size n 30.

c) This question concerns the distributions of sample means. For the distribution of sample means: x = 21 and x = X = 10 = 1.6666 n 36, and the shape would be normal.

For x = 25 z = 25 – 21 = 2.4, 1.6666.  From the z-table P(021) = 0.5 – P(0(3-3.1)/0.4)  =P(z>-0.25) =1-0.4013 (from z table) =0.5987

d) Sample size,n= 64 mean remains same 3.1
standard error of the mean (standard deviation of sample means) expected to be = s/vn = 0.4/v64 = 0.4/8 =0.05 expected shape of the distribution of sample means will be bell shaped as this is normally distributed.

g) If a random sample of 64 customers is selected, the probability that the sample mean would exceed 3 minutes=P(x>3) =P((x-µ)/e >(3-3.1)/0.05) =P(z>-2) =1-0.0228 (from z table) =0.9772.

Order a unique copy of this paper
(550 words)

Approximate price: $22

Basic features
  • Free title page and bibliography
  • Unlimited revisions
  • Plagiarism-free guarantee
  • Money-back guarantee
  • 24/7 support
On-demand options
  • Writer’s samples
  • Part-by-part delivery
  • Overnight delivery
  • Copies of used sources
  • Expert Proofreading
Paper format
  • 275 words per page
  • 12 pt Arial/Times New Roman
  • Double line spacing
  • Any citation style (APA, MLA, Chicago/Turabian, Harvard)

Our guarantees

At Solution Essays, we are determined to deliver high-quality papers to our clients at a fair price. To ensure this happens effectively, we have developed 5 beneficial guarantees. This guarantees will ensure you enjoy using our website which is secure and easy to use.

Money-back guarantee

Most companies do not offer a money-back guarantee but with Solution Essays, it’s either a quality paper or your money back. Our customers are assured of high-quality papers and thus there are very rare cases of refund requests due to quality concern.

Read more

Zero-plagiarism guarantee

All our papers are written from scratch and according to your specific paper instructions. This minimizes any chance of plagiarism. The papers are also passed through a plagiarism-detecting software thus ruling out any chance of plagiarism.

Read more

Free-revision policy

We offer free revisions in all orders delivered as long as there is no alteration in the initial order instruction. We will revise your paper until you are fully satisfied with the order delivered to you.

Read more

Privacy policy

All data on our website is stored as per international data protection rules. This ensures that any personal data you share with us is stored safely. We never share your personal data with third parties without your consent.

Read more

Fair-cooperation guarantee

Ordering and sending money to us is an indication that you are purchasing our products and services. To have business talks laid out in the official language, you can check on our terms and conditions and get more information about this.

Read more

Calculate the price of your order

550 words
We'll send you the first draft for approval by September 11, 2018 at 10:52 AM
Total price:
$26
The price is based on these factors:
Academic level
Number of pages
Urgency
Order your essay today and save 30% with the discount code: LEMONADEPlace Order