BINOMIAL MEAN &
STANDARD DEVIATION
Section 6.3C
It is estimated that 28% of all students enjoy math. If 30
people are selected at random, find the probability that
a.
b.
c.
exactly 18 enjoy math.
at least 24 enjoy math.
Between 17 and 28 enjoy math.
Mean
• If 90% of all people between the ages of 30 and 50 drive
a car. Find the mean number (expected #) who drive in a
sample of 40.
Formulas
Mean :
  np
Variance :   npq
2
St.Dev. :
  npq
If 8% of the population carry a certain gene, find
the expected number who carry the gene in a
sample of 80. Find the standard deviation.
A club has 50 members. If there is a 10% absentee
rate per meeting, find the mean, variance, and
standard deviation of the number of people who will
be absent form each meeting.
GEOMETRIC
DISTRIBUTION
Geometric – “Go Until”
40% of a large lot of electrical components are
from ABA Company. If the components are
selected at random, what is the probability that a
component from ABA will not be selected until
the third pick?
Let’s derive a formula!
Geometric Distribution Formula
p( x)  (1  p)
x 1
p
Flip a coin, what’s the probability that the 1st head
occurs on the 4th trial?
A batter has a 0.295 chance of getting a hit. Find
the following probabilities:
*doesn’t get a hit until his fourth time at bat
*Gets his first hit on one of his first three times at bat
*Doesn’t get a hit until after his third attempt
The Probability that a person is colorblind is 8%.
Find the probability that a colorblind person ..
*is found on the sixth interview
*is found before the second interview
Is found among the first four interview
Is found after four interviews.
Geometric Mean
• If Y is a geometric random variable with probability of
success p on each trial, then its mean (expected value) is
1
𝐸 𝑌 = 𝜇𝑥 = .
𝑝
• That is, the expected number of trials required to get the
first success is
1
.
𝑝
Suppose you roll a pair of fair, six-sided dice until
you get doubles. Let T = the number of rolls it
takes.
• Find the probability that we roll doubles on the 3rd roll.
• In the game of Monopoly, a player can get out of jail free by
rolling doubles within 3 turns. Find the probability that this
happens.
• What is the expected number of trials required to get
doubles?
Homework
• Worksheet