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 pounds 1.3 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 pounds 1.3 pounds

Hardwood Tree Heartwood Diameter 4 cm 1.8 cm

Average Life Expectancy American Male (sample of size n=100) 76 years 1.5 years

Life Expectancy American Female (sample of size n=100)

78 years 1.5 years

Standard normal (unitless!) 0 1

• 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 timeSpitz 2.012 Phelps 1.867Hall 2.048 Laszlo 1.878

Backhaus 2.054 Takeshi 1.883Delgado 2.077 Moss 1.906

Fassnacht 2.078 Peng 1.906Hargitay 2.078 Pawel 1.910Flockner 2.089 Kaio 1.912Meeuw 2.093 Nikolay 1.919

1972 =

2.066 2008 =

1.898

1972 =

0.027 2008 =

0.019

Men’s 200 meter butterfly (finals)

Spitz z – score Phelps z – score100 fly –1.68 –1.4

200 free –1.34 –1.92

• 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 P5, 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.