# Applications of the Normal Distribution

For your initial post, choose one of the following two prompts to respond to. Then In your two follow up posts, respond at least once in each option. Use the discussion topic as a place to ask questions, speculate about answers, and share insights. Be sure to embed and cite your references for any supporting images.

Option 1:

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Use the NOAA data set provided, to examine the variable DX32. DX32 represents the number of days in that month whose maximum temperature was less than 32 degrees F. The mean of DX32 during this time period was 3.6.

Using Excel, StatCrunch, etc., draw a histogram for DX32. Does this variable have an approximately normal (i.e. bell-shaped) distribution? A normal distribution should have most of its values clustered close to its mean. What kind of distribution does DX32 have?

Take a random sample of size 30 and calculate the mean of your sample. Did you get a number close to the real mean of 3.6? Although few individual data values are close to 3.6, why could you expect that your sample mean could be? Be sure to include the mean that you calculated for your random sample.

Imagine that you repeated this 99 more times so that you now have 100 different sample means. (You don’t have to do this … just imagine it!). If you plotted the 100 sample means on a histogram, do you think that this histogram will be approximately normal (bell-shaped)? How can you justify your answer?

Option 2:

Flip a coin 10 times and record the observed number of heads and tails. For example, with 10 flips one might get 6 heads and 4 tails. Now, flip the coin another 20 times (so 30 times in total) and again, record the observed number of heads and tails. Finally, flip the coin another 70 times (so 100 times in total) and record your results again.

We would expect that the distribution of heads and tails to be 50/50. How far away from 50/50 are you for each of your three samples? Reflect upon why might this happen?

In response to your peers, comment on the similarities and differences between yours and your classmate’s data analyses. In particular, compare how far away you and your classmate are from 50/50 for each of your three samples.

To complete this assignment, review the Discussion Rubric document.

WEEK 2 DISCUSSION BOARD PROMPT

For the discussion boards, two options are given for you to choose from for your initial post. In your response posts, you are required to respond at least once to each option. This means you should have a minimum of three posts in total:

1. Your initial post to either Option One or Option Two
2. A response to one of your peers’ responses to Option One
3. A response to one of your peers’ responses to Option Two

Please watch the following video for additional help and direction with these posts:

Notes for Discussion Board 2

OPTION ONE NOTES:

• You should discuss the possibilities of non-normal distributions and/or outliers.
• You should provide embed images of your output from StatCrunch or Excel to supplement your discussion board post.
• You should view this video on how to sample in StatCrunch

OPTION TWO NOTES:

• Be sure to use specific statistic language such as P1, P2 in your posts.

USING MYSTATLAB

Additionally, I wanted to remind everyone know that it is possible to get 100% of the points on every homework this semester. MyStatLab has the options of “Similar Question” when you have completed a problem, which enables you to re-do the problem to score all the points available to you.

For example, suppose question 1 has parts A, B, and C. You correctly answer parts A and B, but incorrectly answer part C. Therefore, for your overall score for this problem, you get partial credit and not the full amount of points. If you select “Similar Question” (located on the bottom right-hand side of the screen in MyStatLab), the program gives you a problem very similar to the one you just solved and allows you to complete the problem again in order to score all the points.

1st classmate response needed

## 2-1 Discussion:Option 1

Jeffrey Pickett posted Sep 10, 2020 2:28 PM

Does this variable have an approximately normal (i.e. bell-shaped) distribution?

This data does not produce a bell shaped, normal distribution.

What kind of distribution does DX32 have?

Skewed right, positive distribution.

Did you get a number close to the real mean of 3.6?

Upon random sampling, I received a mean of 2.267, which given the complete data set, I’d say is “close” to the mean of 3.6.

If you plotted the 100 sample means on a histogram, do you think that this histogram will be approximately normal (bell-shaped)? How can you justify your answer?I would expect the histogram to be more normal. The straight data has an extreme amount of 0s; when averaging random samples of 30 there is a significantly higher chance that averaged samples are more concentrated toward the mean of the total set of 3.6 than 0.

2nd classmate response needed

## Application of the Normal Distribution

Megan Rebele posted Sep 10, 2020 1:15

I chose option 2 for this week because, real fact, it was fun to do and I could engage my children in helping mom with school work(like I help them). We laughed and enjoyed time as a family while flipping coins and keeping track. Statistics should be fun right? As we talked about this before we started (yes I included them in this whole process), they agreed it should be 50/50. Here are the results of the 3 samples we used of 10, 30 , and 70 flips.

• 10 (70/30)
• 7 tails
• 30 (60/40)
• 12 tails
• 70 (56/44)
• 39 tails

This makes me think of the first discussion with the iPhone vs. Android. As we look at a smaller number, one or two flips can alter the numbers. The lower the amount of data points included in your calculations, the more it will change the outcome. The more times we flipped the coins the closer we got to a 50/50 split. This showed us that the smaller amount of flips was not an accurate representation of a 50/50 split. At this point we had to continue flipping to see when we would achieve the exact 50/50 split we were looking for. The number we got was 138 flips with 69 tails and 69 heads. With 70 flips we were not off by very much but almost had to double it to achieve the 50/50 numbers because the larger the sample size, the smaller each data point affects the overall outcome. I hope everyone had as much fun this week as I did!

Megan

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