Statistics 101: Examples of continuous R. V.

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Examples of normal random variables

• "Blue ribbon panel" predicts GNP growth will be 3.25% next year. Typical error 2%. What is the probability of "negative growth?"

• Intel produces 10,500 chips a day. On average 6300 pass the burn in test, with a standard deviation of 50. Any line manager who has fewer than 6000 passed tests is fired. What is the chance of this happening by chance alone?

  How would we have determined the SD if were weren't told its value?

• In a 10 person "devil take the hindmost" race, if you are in the bottom 10% for speed, you will lose the first lap. Suppose the mean speed for the race is 30 mph with a standard deviation of .1 mph. How fast is the bottom 10% going?

• A 15 oz box of Captain Crunch should contain at least 15 oz, most of the time. The filling machine has a SD of .1 oz. General Mill's wants to besure that 99% of the boxes are filled full enough. What should they set the mean production level for the machine to be?

Approximations

• Approximating the binomial by a normal

• Approximating the Poisson by a normal

• Why can't we approximate a geometric by a normal?

General approximations

• Approximating the sum of anything by a normal

• called the "Central Limit Theorem" or CLT

• Generally used in taking averages;
  • What is the average height
  • What is the weight of a widget
  • What is the average number of bad tracks on a hard disk?
  • etc