# Due tomorrow, 5/19/19- Applications of the Normal Distribution

Due tomorrow 5/19/19- 1 page minimum

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For your initial post, choose one of the following two prompts to respond to.

Option 1:

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?

OR

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?

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