Transcript Slide 1

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?!?!?!?!
• 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)?
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 “superior” (that is, have
an IQ above 130)?
• 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.