Statistics Mathematicians Unit 2

• A popular anecdote about Johann Carl Friedrich Gauss (1777 – 1855) involves “Little Gauss Formula” which he discovered in primary school when the teacher gave the class the task to sum up all the integers from 1 to 100 as punishment.
• Gauss is called the “Titan of Science” and the “greatest mathematician since antiquity” since he made remarkable and significant contributions which included normal density function. This is the reason why normal distribution is also called the Gaussian distribution.
• In 1733, the French mathematician Abraham De Moivre derived an equation for a normal distribution based on the random variation of the number of heads appearing when many coins were tossed.
• Abraham De Moivre


  He is famous for predicting the day of his own death. He found that he was sleeping 15 minutes longer each night. He calculated that he would die on the day that he slept for 24 hours.
• Karl Pearson is an English mathematician who became known as the founder of modern statistics because of his contribution to this field.
• Pierre Simon Marquis de Laplace (France) and Carl Friedrich Gauss (Germany), derived the equation of the normal curve independently and without any knowledge of De Moivre’s work.
• The curve of the normal distribution is bell-shaped.
• The mean, median, and mode are equal and are located at the center of the distribution.
• If the mean is 0 and the standard deviation is 1, then the normal distribution is a standard normal distribution.
• The larger the standard deviation, the more dispersed, or spread out, the distribution is.
• Empirical Rule is the approximation of proportions within a normal

  distribution.

  
• The average Pag-ibig salary loan of IT administrators is ₱23,090 monthly. If the debt follows a normal distribution with a standard deviation of ₱2,500, find the probability that the IT administrator owes less than ₱16,500. What is X?

  16, 500

  
• The average Pag-ibig salary loan of IT administrators is ₱23,090 monthly. If the debt follows a normal distribution with a standard deviation of ₱2,500, find the probability that the IT administrator owes less than ₱16,500. What is the µ?

  23,090
• The average Pag-ibig salary loan of IT administrators is ₱23,090 monthly. If the debt follows a normal distribution with a standard deviation of ₱2,500, find the probability that the IT administrator owes less than ₱16,500. What is the σ?

  σ = 2,500