lab8.mws Lab Overview Definitions Probability Density Function (pdf) Mean Variance Cumulative Distribution Function (cdf) Properties of pdf's and cdf's Example 1 (a) What percentage of the calls last between 1 and 2 minutes? (b) What percentage of calls last 1 minute or less? (c) What percentage of calls last 3 minutes or more? (d) Find the cumulative density function (cdf). Example 2 (a) Find a. (b)Find P, the cdf. (c) Find the median and mean time gap. (d) Sketch the graphs of the pdf and cdf. Example 3 (a)(i) Sketch graphs of  the pdf for the normal distribution with fixed mu (say mu = 5) and varying sigma (say, sigma = 1, 2, 3) . (a)(ii) Sketch graphs of the pdf for the normal distribution with varying mu (say mu = 4, 5, 6) and fixed sigma (say, sigma = 1). (b) Explain how the graphs confirm that mu is the mean of the distribution and that sigma is a measure of how closely the data is clustered around the mean. Example 4 (a) Show that p has a maximum at mu. What is the maximum value? (b) Show that p has inflection points at mu+sigma and mu-sigma. (c) Describe in your own words what mu and sigma tell you about the distribution. Lab Questions Hints and Notes: Bonus Questions 1. [4 points] 2. [3 points]