6.2 Binomial Probability Distribution. Objectives: By the end of this section, I will be able to… Explain what constitutes a binomial experiment. Compute probabilities using the binomial probability formula. Find probabilities using the binomial tables.
By the end of this section, I will be
Only two outcomes possible
Fixed number of trials
Outcomes are independent of one another
Probability of a success remains the same for each trial
Ask yourself the four questions.
Are there 2 outcomes?
NOT a Binomial Dist.
Is there a fixed number of trials?
Are the outcomes independent?
Does the probability remain the same for any trial?
p(success) = p
p(failure) = q
n = total number of trials
x = selected number out of total
1) What is the probability that exactlyseven of you passed the quiz?
4) What is the probability that at most three of you passed the test?
5) What is the probability that at least nineteen of you passed the test?
This is the same as saying “exactly4.”
This is the same as saying “at most 2.”
n = total number
p = probability of success
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
mean = 600(1/6) = 100
variance = 600(1/6)(5/6) ≈ 83.333
n = total number = 500
p = p(success) = p(cancel) = 7%
q = p(failure) = p(not cancel) = 93%
mean = 500(7%) = 35
variance = 500(7%)(93%) = 32.55