Pace University Math 117 Instructor: Vinh Ly

Spring 2018 Data Analysis Project April 4th, 2018 Final Proiect Conceptual Problems: Probability Density Function and Binomial Convergence

Problem 1 a/Use Excel/Megastat to find the discrete probability and cumulative probability of the

Binomial distribution with probability of success p = 0.4 and n = 60. Find its mean and variance. b/Based upon the chart on Excel, what can you conclude about the binomial convergence?

Hint: Use binom.dist function on Excel and sketch the curve.

Problem 2 Use Excel/Megastat to create the density probability plot of normal distribution. Take u = 60

and o = 5. Set up the range values ofx from 40 to 80. Hint: Use norm.dist function and sketch the curve with tick = 0.1

Problem 3 (extra credit) Demonstrate the Central Limit Theorem{CLT) of the sample mean by sampling a 100 uniform

distribution data with 50 variables. Verify the result by computing the sample mean, sample

variance and sketch the histogram on Excel/Megastat. Hint: Generate 100 datasets of 50 variables and calculate 50 sample means to determine the

distribution of? and 52. Practical Problems: Historical Trends and Patterns in Stock Prices Choose two publicly traded companies with a sample size of 50 and a time range {long

term/short term) for its stock prices so that you can download the data from quote.yahoo.com

or google.com/finance. Make sure to STATE the COMPANY HISTORY and WHY YOU PICK THESE

2 STOCKS for comparison. Problem 4 Use a statistical package {Excel/Megastat) to find the summary measurements: min, max, mean,

median, standard deviation of the historical prices of 2 stocks a/Draw a Box Plot for both stocks that you picked. Identify the highest and lowest stock prices.

b/Repeat this exercise with histogram/bar-charts and scatter plots for each stock. c/Write a short paragraph describing how the two stock prices are different. Hint: Base your

answer on any notable differences you observe in the two Box Plots.