# (Solution) MATH 399N Week 5 Discussion: Interpreting Normal Distributions

Required Resources

Read/review the following resources for this activity:

• Textbook: Chapter 6 (All Sections)
• Lesson
• Minimum of 1 scholarly source

Initial Post Instructions

Log onto website where you can observe your service bill for the last 12 months (electric bill, cell phone bill, water bill, etc.). If you do NOT feel comfortable sharing this data, you can make up values.

1. In excel, list the values of your bill for the last 12 months on one column.
2. Find the sample mean and sample standard deviation of your data.
3. Pick three bills from the last 12 months and change the values into z-scores. What does the z-score tell you about that particular month?

Analysis

1. Between what two values would be considered a normal bill? Remember, being within 2 Standard Deviations is considered normal.
2. Are any of your bills in the last 12 months unusual? Very unusual?
3. Are there times when you would accept an “unusual” bill? Explain.

Follow-Up Post Instructions

Respond to at least two peers or one peer and the instructor. Further the dialogue by providing more information and clarification.

Here are some suggested responses–

1. Compare and contrast your post with a post of a peer.
2. Explain what you learned by participating in this week’s discussion.

Solution:

I decided to check my electric bill for the past year, and I rounded my bill up or down so these are not the exact numbers from my bill. To find the sample standard deviation I would use the equation s2=∑(x−samplemean)2n−1s2=∑(x−samplemean)2n−1 and finding the sample mean is the same as finding the mean.

 Month Cost z-score Jan-Feb 55 -0.477 Feb-Mar 65 Mar-Apr 60 Apr-May 95 May-June 120 June-July 170 July-Aug 250 2.19 Aug-Sept 125 Sept-Oct 20 Oct-Nov 15 Nov-Dec 13 -1.05

Sample mean = 89.82

Sample standard variation = 73.04

When I changed three of the bills to z-scores, it shows how many standard deviations from the mean that number is (Statistics how to, n.d.).  For the month of January, my sd is -0.477 and it is..Please click the icon below to purchase full answer at only \$5