Transcript PowerPoint from Class

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.
Men’s 200 meter butterfly (finals)
1972 times (minutes)
Spitz
Hall
Backhaus
Delgado
Fassnacht
Hargitay
Flockner
Meeuw
1972 =
1972 =
time
2.012
2.048
2.054
2.077
2.078
2.078
2.089
2.093
2.066
0.027
2008 times (minutes)
Phelps
Laszlo
Takeshi
Moss
Peng
Pawel
Kaio
Nikolay
2008 =
2008 =
time
1.867
1.878
1.883
1.906
1.906
1.910
1.912
1.919
1.898
0.019
Spitz z – score Phelps z – score
100 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.