Transcript Binomial Distribution formula

x
C
p
q
n x
n x
WARM UP
Eighty six percent of seniors got drunk on New Year’s
Eve night (hope you had fun at Steve Bart’s House!).
There are seven seniors walking down the hallway.
1) Find the probability that exactly four of them were
WASTED.
2) Find the probability that at least five of them were
WASTED.
Binomial Distribution formula
p(success) = p
p(failure) = q
n = total number of repeated trials
x = selected number of successes
x
C
p
q
n x
n x
Section 6.6
Finding the MEAN, VARIANCE,
and STANDARD DEVIATION
of a Binomial Distribution
Mean of the Binomial Distribution
x = mean
n = total number
p = probability of success
x  np
Variance and Standard Deviation

The variance of a binomial distribution is:
variance  npq

The standard deviation of a binomial distribution is:
s.d .  variance  npq
DICE GAMES
1) A die is rolled 600 times. Find the mean,
variance, and standard deviation of the
number of 4’s that are rolled.
n = total number = 600
p = p(success) = p(4) = 1/6
q = p(failure) = p(not 4) = 5/6
 npq= 600(1/6) = 100
xvariance
 np mean
s.d .variance
 variance

npq
83.3333  9.1287
= 600(1/6)(5/6) ≈ 83.333
VACATION!!!!
2)
Liberty Travel finds that 7% of all vacation packages are
canceled each year. If they estimate 500 packages a
year, how many can they expect will be canceled (aka
find the mean)?
n
=
total
number
=
500
3) Find the variance and standard deviaton.
p = p(success) = p(cancel) = 7%
q = p(failure) = p(not cancel) = 93%
mean
=
500(7%)
= 35
variance
= 500(7%)(93%)
= 32.55
32.55
 5.705