I am new at a job and I have been given instructions that focused on Population and Sampling Distributions

I need support in proving that the use of z-scores to describe the location of a score within a distribution and to standardize scores from different populations. In addition to that, I also need to explain basic probability rules and relate them to a frequency distribution through the use of z-scores.

There is need to specify how a sampling distribution is different from a population distribution and the relationship between standard deviation and sampling error. Use t-scores to describe the location of scores with a t-distribution.

I can use either of the following materials as guide or other materials

Grove, S. (2007). Statistics for health care research: a practical workbook. (1st ed.). St. Louis, MO: Elsevier. ISBN-13: 9781416002260 (Includes only Exercises 16, 29, 31, 36, 27 and 40)

Burns, N., & Grove, S. (2011). Understanding nursing research: Building an evidence-based practice. (5th ed.). St. Louis, MO: Elsevier. ISBN-13: 9781437707502 (Includes only chapters 9 and 11)

My instructions were to provide solutions using the context materials in exercise 29

1) I need help in solving the problems that may be faced at work in relation toExercise 29 in Statistics for health care research: a practical workbook

2) I need to complete the study questions about the reading and check my solutions to the study questions.

3) Afterwards, I need to copy and paste the Exercise 29: Questions in page 224 into a word document.

4) The Word's equation editor has to be used, etc., and provide a short written description as to how the final result is obtained.

Population and Sampling Distribution Excel Worksheet

1) Please check the Population and Sampling Distribution Excel Worksheet: AATACHED

2) Finally, I need all my solutions to the questions on the Excel document.

The solution provides step by step method for the calculation of Z score and probability using the Z score. Formula for the calculation and Interpretations of the results are also included.

A retailer's sale in widgets is normally distributed over the time of one year. The mean of the sales is 141.1 with a standard deviation of 13.62. What is the probability that he will not be able to sell 160 or more widgets in the next year?

A normal population has an average of 80 and a standard deviation of 14.0.
Calculate the probability of a value between 75.0 and 90.0.
Calculate the probability of a value of 75.0 or less.
Calculate the probability of a value between 55.0 and 70.0.

Given a standard normal distribution, determine the following: Show Table values used.
Given a standard normal distribution, determine the following: Show Table values used.
a) P( Z < 1.32) =?
b) P(Z>1.32) = ?
c) P(Z<-1.32) =?
d) P(-.30

Question: A set of 50 data values has a mean of 40 and a variance of 25.
I. Find the standard score (z) for a data value = 47.
II. Find the probability of a data value > 47.
III. Find the probability of a data value < 47.
Show all work.

Individual scores of a placement examination are normally distributed with a mean of 84.2 and a standard deviation of 12.8.
If the score of an individual is randomly selected, find the probability that the score will be less than 90.0.
If a random sample of size n = 20 is selected, find the probability that the sample mean

A normal distribution has a mean of u= 40 and o=10. if a vertical line is drawn through the distribution at x= 55, what proportion of the scores on the right side of the line?
A normal distribution has a u= 80 and o= 10. what is the probability of randomly selecting a score greater than 90 from this distribution?
A normal

The standard normal table shows an area value of 0.1 for a z-score of 0.25 and an area value of 0.35 for a z-score of 1.04. What percentage of the observations of a random variable that is normally distributed will fall between 0.25 standard deviations below the mean and 1.04 standard deviations above the mean?
a. 25%
b. 35%

A normal distributed population has a mean of 250 pounds and a standard deviation of 10 pounds. Given n = 20, what is the probability that this sample will have a mean value between 245 and 255 pounds?

Discuss the difference between a z-score and the area under the normal curve. What exactly does a z-score represent? What does the area under the graph of a normalprobability distribution represent? Can a z-score be negative? Can an area be negative?