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CP Statistics
Miss Sciandra
8.1 Binomial Distribution
Name____________________
Date______Pd_______
A Binomial Distribution results from a data set that meets all of the following requirements:
1. ________________________________________________________________________
________________________________________________________________________
2. ________________________________________________________________________
3. ________________________________________________________________________
4. _______________________________________________________________________
_______________________________________________________________________
Example 1: Blood type is inherited. If both parents carry genes for the O and A blood types,
each child has a probability of 0.25 of getting two O genes and so of having blood type O. The
number of O blood types amongst 5 children of these parents is the count, x, of successes in 5
independent observations with the probability of 0.25 of a success on each observation.
Does this setting meet the requirements to be a Binomial Probability Distribution? Show all 4
requirements apply.
Example 2: Deal 10 cards from a shuffled deck and count the number X of red cards. There are
10 observations, and each gives either a red or black card.
Is this a binomial distribution? Show all 4 requirements apply.
Finding Binomial Probabilities
*Note:______________________________________________________________
1) Discrete
2) Continuous
_____________________________
___________________________
_____________________________
___________________________
Where to find:
*The
inequality
symbol
counts!*
CP Statistics
Miss Sciandra
8.1 Binomial Distribution
Name____________________
Date______Pd_______
Example 3: An engineer selects an SRS of 10 switches from a large shipment for detailed
inspection. Unknown to the engineer, 90% of the switches in the inspection pass to meet the
specifications.
a) What is the probability that 5 of the 10 switches in the sample pass inspection?
b) What is the probability that 8 of the 10 switches in the sample pass inspection?
c) What is the probability that 5 or 6 of the switches in the sample pass inspection?
d) What is the probability that no more than 1 of the 10 switches in the sample fail inspection?
*e) What is the probability that less than 7 switches in the sample fail inspection?
Example 4: A 10-question multiple choice exam is given, and each question has five possible
answers. Ryan takes this exam and guesses at every question. Use the binomial distribution to
find the probability that
a) He gets exactly 3 questions correct
*c) He gets at least one question correct
b) He gets no questions correct
*d) He gets at least 9 questions correct
Mean, Variance, and Standard Deviation- Binomial Distribution
𝝁=
𝝈𝟐=
𝝈=
CP Statistics
Miss Sciandra
8.1 Binomial Distribution
Name____________________
Date______Pd_______
Example 5: An engineer selects an SRS of 10 switches from a large shipment for detailed
inspection. Unknown to the engineer, 90% of the switches in the inspection pass to meet the
specifications.
a) Find the average amount of switches that pass inspection
b) Find the variance and standard deviation of the amount of switches that pass inspection
Check For Understanding:
1. An electronics store has a 30% chance of selling a home theatre center to a particular
customer. If the store has fifteen customers, what is the probability that the store will
make seven sales?
2. Miss Sciandra has twenty students in her class. If each student has a 75% chance of
showing up to class, what is the probability that at most eighteen students show up to the
next class?
3. The probability that Susan will make a particular car sale is 0.05. If Susan talks to ten
customers, what is the probability that she will make no more than 2 sales?
4. Philip has twenty customers that are looking for real estate. The probability that Philip
will make a particular sale is 0.20.
a)What is the probability that he will make at least one sale?
b) find the mean, variance, and standard deviation for the amount of sales