Download 23.D The Binomial Distribution Binomial Probability Distribution

23.D The Binomial Distribution
Binomial Probability Distribution Function
n is the number of trials
p is the probability of a success
1 − p is the probability of a failure
r is the number of successes
n − r is the number of failures
The expected (or mean) outcome of a binomial experiment is:
The variance of a binomial experiment is:
If X is the random variable of a binomial experiment with parameters n and p, then we write
X ~ B ( n, p ) where ~ is read “is distributed as”.
The find the probability that a binomial variable takes a value that is at most r we use the
binomial cumulative distribution function P ( X ≤ r )
Ex1. 72% of union members are in favour of a certain change to their conditions of employment. A
random sample of five members is taken. Find:
a)
the probability that
b)
the probability that
condition
c)
the
members are in favour of the change in conditions
members are in favour of the changed
of members in the sample that are in favour of the change.
Ex2. A fair coin is tossed 20 times.
a)
Calculate the probability of getting
b)
heads
Calculate the probability of getting
heads
Calculate the probability of getting at most
heads.
c)
d)
Ex3. The probability of obtaining heads on a biased coin is 0.4. The coin is tossed 600 times.
a) Would the probability of getting
heads be the same as the probability of getting
heads? Explain.
b) i) Write down the mean number of heads.
ii) Find the standard deviation of the number of heads.
c) Find the probability that the number of heads obtained is less than one standard deviation away
from the mean.
Ex Last: Fezzick drops a marble into the sorting machine that is set such that the probability it will
2
fall to the left of each peg is . He wins the amount of money that is written on the box that the ball
3
lands in.
$1
$2
$4
$8
$16
$100
How much should Count Rugen charge Fezzick to play the game if he wants it to be a fair game?
ANSWERS:
4d. 1.1875
6d. 8.57
6e. 0.321
HW: p.642 #1bcd, 3, 4, 6, 7 Plus:
4d. What is the variance in the number of apples that have a blemish?
6d. Find the standard deviation for the number of students that will be absent from school
next week?
6e. Find the probability that the number of students absent next week is more than one
standard deviation away from the mean.