In this module, you explore the normal distribution. A standard normal distribution has a mean of zero and standard deviation of one. The z-score statistic converts a non-standard normal distribution into a standard normal distribution allowing us to use Table A-2 in your textbook and report associated probabilities.
This discussion combines means, standard deviation, z-score, and probability. You are encouraged to complete the textbook reading and start the MyStatLab Homework before starting this discussion.
The following table reports simulated annual flying squadron costs (in millions of dollars) at the following locations:
Text description of the Annual Squadron Flying Costs in Millions (PDF)
Use Microsoft Excel and StatDisk to complete the Flying Squadron Costs table for the aircraft type listed below:
- Complete the costs using the B-52 data; use the Kadena data point in your z-score and probability calculations.
Report your values to two decimal places (i.e., 0.12) except for probability. Report probability values to four decimal places (i.e. p = 0.1234).
Your StatDisk results should look similar to this image:
Post & Discuss
Post the images of your spreadsheet and StatDisk results in the discussion area along with a narrative of your findings and the responses to the questions below.
- Do these costs appear to come from a population that has a normal distribution? Why or why not?
- Can the mean of your data sample be treated as a value from a population having a normal distribution? Why or why not?
- Did an “unusually low” or “unusually high” z-score value occur?
- Was the associated z score probability value less than 0.05 (p < 0.05); meaning a “significantly low” or “significantly high” event? If yes, what are the implications for the base and/or aircraft?
- What were your findings? Hint: focus on the calculated mean, standard deviation and z-score (include probability) to interpret your results.