Assume a binomial distribution has p = ½. Let’s look at some of its probability distributions for a variety of numbers of trials...

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Presentation transcript:

Assume a binomial distribution has p = ½. Let’s look at some of its probability distributions for a variety of numbers of trials...

n = 3

n = 5

n = 10

n = 25

n = 50

n = 100

Hey! What about ME?!?!?!?!

Some Means and Standard Deviations of some Normally Distributed (“bell – shaped”) Data Sets!  American Newborn Weight 7.5 pounds1.3 pounds A former student weighed 2.3 pounds at birth. How many standard deviations below average was she? How about on the other end of the spectrum?

Some Means and Standard Deviations of some Normally Distributed (“bell – shaped”) Data Sets!  American Newborn Weight (2.3 #? Guinness?) 7.5 pounds1.3 pounds Hardwood Tree Heartwood Diameter 4 cm1.8 cm Average Life Expectancy American Male (sample of size n=100) 76 years1.5 years Life Expectancy American Female (sample of size n=100) 78 years1.5 years Standard normal (unitless!) 01

Adult IQ is normally distributed with a mean of 100 and a standard deviation of 15. What percent of adults are “dull normal” (that is, have an IQ between 80 and 90)? It’s a slightly antiquated term, but let’s go with it for now.

1972 times (minutes) 2008 times (minutes) time Spitz2.012 Phelps1.867 Hall2.048 Laszlo1.878 Backhaus2.054 Takeshi1.883 Delgado2.077 Moss1.906 Fassnacht2.078 Peng1.906 Hargitay2.078 Pawel1.910 Flockner2.089 Kaio1.912 Meeuw2.093 Nikolay1.919  1972 =  2008 =  1972 =  2008 = Men’s 200 meter butterfly (finals)

What percent of adults are “dull normal” (that is, have an IQ between 80 and 90)? What percent of adults are “extremely low” (that is, have an IQ below 70)? This is the “MII” range’s new labeling. What do you have to score to get into MENSA?

The length of human pregnancies from conception to birth varies (roughly) according to a distribution that is approximately normal with a mean of 266 days and a standard deviation of 16 days. What is the cutoff for the shortest 5% of all pregnancies? This is P 5, and births shorter than these are called premature births. Labor is usually induced if an expectant mother has exceeded her due date by 2 weeks. Find the probability that a pregnancy will last more than 2 weeks past the due date.