Download Lesson 6.6 Computing Mean and Standard Deviation of a Binomial

Lesson 6.6 Computing Mean and Standard Deviation of a
Binomial Distribution Notes
Statistics
Page 1 of 3
Describing the distribution of discrete data:
 Mean,  :
o Also called the Balance Point
o Expected value of the number of successes
o   np is the expected number of successes for the random variable r
 r is the random variable representing the number of successes in a
binomial distribution
 n is the number of trials
 p is the probability of success on a single trial
 q is the probability of failure on a single trial
 Standard Deviation,  :
o Also called the measure of the spread of data
o   npq is the standard deviation for the random variable r
 r is the random variable representing the number of successes in a
binomial distribution
 n is the number of trials
 p is the probability of success on a single trial
 q is the probability of failure on a single trial
Example 1: For a binomial distribution with n=5 and p=0.4, find  and  .
Example 2: Johnny enjoys playing basketball. He figures that he makes about 50% of
the field goals he attempts during a game. In today’s game, he shot 6 field goals.
What is the expected value? What is the standard deviation?
Lesson 6.6 Computing Mean and Standard Deviation of a
Binomial Distribution Notes
Statistics
Page 2 of 3
Example 3: Suppose you are to throw a fair coin 3 times. Make a histogram showing
the probability that the Head will appear 0, 1, 2, and 3 times.
a. This is a binomial experiment with n = ___________ and p = __________.
b. Make a distribution table for this binomial distribution.
c. Make a histogram for this distribution.
d. Find the expected value for the number of successes.
e. Find the measure of the spread of the data.
Lesson 6.6 Computing Mean and Standard Deviation of a
Binomial Distribution Notes
Statistics
Page 3 of 3
Example 4: A waiter at the Blue Restaurant has learned from experience that the
probability that a lone diner will leave a tip is only 0.7. During one lunch hour, the
waiter serves six people who are dining by themselves. Compute the mean and
standard deviation and explain what you have found.
Assignment: p. 234 #1, 2, 7, 9, 11, 13