1. Demonstrate that you understand the basic concepts involving the the normal distribution. In two small paragraphs describe a couple of properties/rules applicable to the normal distribution.
2. Provide an original example of some practical case where we can use the normal distribution (e.g., IQ scores follow a normal distribution of probabilities with a mean IQ of 100 and a standard deviation of 15 IQ points.). Assign your numbers for mean μ and standard deviation σ. Make sure μ is about four times bigger than σ. Then select any number “a” below or above mean μ, but not too far from μ . The difference (a – μ) should be less than 3σ. Your chosen numbers should be different from those chosen from your fellow classmates.
For example, μ = 80, σ = 20, a = 90 (or a = 75).
Find following two probabilities:
1) P(x < a)2) P(x > a)Use the formula z = (a – μ)/σ to calculate your z-value. Please refer to the Appendix Table for the Standard Normal Distribution within the eText to find the desired probabilities.
Hint: To find P(x>a) use formula: P(x>a) = 1 – P(x<a).
3. Describe how you would find P( a < x < b ). Provide an original example to illustrate how you would find such probabilities.