Download 6-6 Binomial Probability - White Plains Public Schools

SWBAT: Compute and interpret probabilities involving binomial random variables.
Lesson 6-6
Do Now:
A sunglasses company sells two distinct brands of glasses. Type A sells 82% of the time for $37.
Type B sells 18% of the time for $87. What is the expected value for each of the sunglasses
sold?
(A) $15.66
(B) $30.34
(C ) $46.00
(D) $62.00
(E) $124.00
How do we determine a BINOMIAL setting??
A binomial setting arises when we perform several independent trials of the same chance
process and record the number of times that a particular outcome occurs. The four conditions for
a binomial setting are:
B
I
inary? The possible outcomes of each trial can be classified as “success” or “failure.”
ndependent? Trials must be independent; that is, knowing the result of one trial must not
have any effect on the result of any other trial.
N
S
umber? The number of trials n of the chance process must be fixed in advance.
uccess? On each trial, the probability p of success must be the same.
SWBAT: Compute and interpret probabilities involving binomial random variables.
Lesson 6-6
BINOMIAL PROBABILITY
Binomial Probability Calculator Steps
binompdf(n,p,k) computes P(X = k)
binomcdf(n,p,k) computes P(X ≤ k)
Example:
Each child of a particular pair of parents has probability 0.25 of having type O blood. Suppose
the parents have 5 children.
(a) Find the probability that exactly 3 of the children have type O blood.
(b) Should the parents be surprised if more than 3 of their children have type O blood? Justify
your answer.
SWBAT: Compute and interpret probabilities involving binomial random variables.
Lesson 6-6
You Try!!
To introduce her class to binomial distributions, Mrs. Desai gives a 10-item, multiple-choice
quiz. The catch is, students must simply guess an answer (A through E) for each
question. Mrs. Desai uses her computer’s random number generator to produce the answer
key, so that each possible answer has an equal chance to be chosen. Patti is one of the students
in this class. Let X = the number of Patti’s correct guesses.
(a) Show that X is a binomial random variable.
(b) Find P(X = 3). Explain what this result means.
(c) To get a passing score on the quiz, a student must guess correctly at least 6 times. Would
you be surprised if Patti earned a passing score? C ompute an appropriate probability to support
your answer.
SWBAT: Compute and interpret probabilities involving binomial random variables.
Lesson 6-6
LESSON PRACTICE
For Questions 1 & 2, explain whether the given random variable has a binomial distribution.
1. Seed Depot advertises that 85% of its flower seeds will germinate (grow). Suppose that the
company’s claim is true. Judy buys a packet with 20 flower seeds from Seed Depot and plants
them in her garden. Let X = the number of seeds that germinate.
2. Exactly 10% of the students in a school are left-handed. Select students at random from the
school, one at a time, until you find one who is left-handed. Let V = the number of students
chosen.
3. In the United States, 44% of adults have type O blood. Suppose we choose 7 U.S. adults at
random. Let X = the number who have type O blood.
(a) Use the binomial probability formula to find P(X = 4). Interpret this result in context.
(b) How surprising would it be to get more than 4 adults with type O blood in the
sample? C alculate an appropriate probability to support your answer.
SWBAT: Compute and interpret probabilities involving binomial random variables.
Lesson 6-6
LESSON PRACTICE
4. Suppose you purchase a bundle of 10 bare-root rhubarb plants. The sales clerk tells you that
on average you can expect 5% of the plants to die before producing any rhubarb. Assume that
the bundle is a random sample of plants. Let Y = the number of plants that die before producing
any rhubarb.
(a) Use the binomial probability formula to find P(Y = 1). Interpret this result in context.
(b) Would you be surprised if 3 or more of the plants in the bundle die before producing any
rhubarb? C alculate an appropriate probability to support your answer.
5. Seed Depot advertises that 85% of its flower seeds will germinate(grow). Suppose that the
company’s claim is true. Judy buys a packet with 20 flower seeds from Seed Depot and plants
them in her garden. Let X = the number of seeds that germinate.
(a) Find the probability that exactly 17 seeds germinate. Show your work.
(b) If only 12 seeds actually germinate, should Judy be suspicious that the company’s claim is
not true? C ompute P(X ≤ 12) and use this result to support your answer.