Download Applications of Mathematics 12

Applications of Math 12
Lesson 2
chapter 3 statistics
Binomial Distributions / binompdf function PART 1
learning outcomes:
1. recall the parameters of a binomial experiment
2. Learn to clear the lists from your memory after you are done
3. use the binompdf function to determine the probability distribution
4. Determine the probability of
a. EXACTLY a certain number binompdf(n, p x)
b. At MOST a certain number
binomcdf(n, p, x) PART 2
c. At LEAST a certain number
1- binomcdf(n, p, x-1). PART 2
1. Recall from chapter one: a Binomial experiment satisfies the following four conditions:
1. The experiment consists of n identical trials.
2. Each trial results in one of the two outcomes, called success and failure.
3. The probability of success, denoted p , remains the same from trial to trial.
4. The n trials are independent. That is, the outcome of any trial does not affect the outcome
of the others.
2. To clear lists: 2nd
MEM
3. Recall from last day : go into
4: clrAllLists
2nd
DISTR
VARS
(top of the
button)
To Generate a Binomial Distribution and put it in LISTS so you can graph the histogram
1.
0: Binompdf(# of trials, Probability of Success on each trial)
Example: rolling 5 die and recording the number of 3s, enter:
(success = a 3, failure = something else)
nd
 Store the results in list L2, STO  2 #2
 Enter the Outcomes 0, 1, 2, 3, 4,5 in L1
Number
 Record your results in the table.
of 3s
 Interpret your results.
0
 graph it on the calculator
1
2
3
4
5
1
binompdf(5, (1/6))
Probability
Applications of Math 12
chapter 3 statistics
This function can help us answer questions like
“What is the probability that exactly _____ will appear”
Example 1: The probability of a cure for heart disease is 80% if a new experimental drug is
used. If two people experiment in taking this drug, Create a probability distribution for this
problem using the TI-83.
# of survivors
Probability
This is a binomial experiment because there are only
0
two possible outcomes:
success ___________________
1
failures ___________________
2
Enter binompdf(2, 0.8) (2 trials, P(success)= 0.8)
(0 = no survivors, 1 = exactly 1 survivor, and 2 = exactly two survivors)
a) what is the probability that both will survive? ____________
b) what is the probability that neither will survive? ____________
c) what is the probability that exactly one will survive? ____________
Example 2: The probability of Mr. X getting a hit from a throw in baseball is 0.25. Create a
probability distribution for 3 throws
# hits
0
Probability
a) What is the probability that Mr. X will get exactly
2 hits in 3 throws? ____________
1
2
3
b) What is the probability that Mr. X will get exactly
1 hit in 3 throws? ____________
c) What is the probability that Mr. X will get at least 2 hits in 3 throws? ____________
d) What is the probability that Mr. X will get at most 2 hits in 3 throws? ____________
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Applications of Math 12
chapter 3 statistics
SUMMARY: binompdf( n, p) can be useful to answer many questions about
the distribution, but you have to store it in L2, fill in L1 and look at all the
probabilities.
IF YOU ONLY HAVE ONE QUESTION to answer, there are faster ways.
To find exactly x successes in n trials, type binompdf(n, p, x)
Try example 2 again:
a) What is the probability that Mr. X will get exactly 0 hits in 3 throws? ____________
b) What is the probability that Mr. X will get exactly 1 hit in 3 throws? ____________
c) What is the probability that Mr. X will get exactly 2 hits in 3 throws? ____________
d) What is the probability that Mr. X will get exactly 3 hits in 3 throws? ____________
********************************************************************************
EXAMPLE 3: A certain champion bowler gets a “strike” 4 times out of 6 attempts.
(a)
What is the probability of them getting exactly 8 strikes in 10 attempts?
(b)
What is the probability of them getting NO “strikes” in 10 attempts?
(c)
What is the probability of them getting at least one “strike” in 10 attempts?
EXAMPLE 4: Suppose there is a 75% chance that a customs officer will ask to inspect your
luggage upon entering Canada. For 100 randomly selected traveler entering Canada,
a) What is the probability that exactly 60 will have their luggage inspected?
(Three decimal places)
b) What is the probability that NOBODY will have their luggage inspected?
(Three decimal places)
c) What is the probability that at least one person will have their luggage inspected?
(Three decimal places)
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Applications of Math 12
ASSIGNMENT :
1.
chapter 3 statistics
Binompdf (n, p, x)
name: ____________________
The probability of “success” for an event is 0.65. What is the probability of
exactly 14 “successes” in 20 trials?
0.17
2.
The probability of “success” for an event is 0.8. What is the probability of
exactly 5 “successes” in 10 trials?
0.03
3.
The probability of “success” for an event is 0.75. What is the probability of
exactly 3 “successes” in 6 trials?
0.13
4.
15% of coins currently in circulation were made before 1980. What is the
probability that in a random sample of 200 coins exactly 40 of them were made
before 1980?
0.011
5.
20% of students at a certain school smoke cigarettes. What is the probability
that in a random sample of 10 students, exactly 4 of them will smoke?
0.09
6.
15% of travellers passing through a customs point are checked. What is the
probability that exactly 60 travellers will be checked out of 100 randomly
selected travellers?
0
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Applications of Math 12
7.
chapter 3 statistics
A certain basketball player makes a free throw 5 times out of 8 attempts. What
is the probability that they will make exactly 2 throws out of three attempts?
0.44
8.
binompdf(3, (5/8), 2)
A certain darts player can hit the bulls-eye 4 times in 10 attempts. What are the
chances that they can hit the bull exactly 10 times out of 15 attempts?
0.02
9.
The probability of a certain baseball player getting a hit on a fair throw is 0.65.
What is the probability that they will get exactly 4 hits out of 5 fair throws?
0.31
10. The probability that a bowler will get a “strike” is 0.7. What is the probability
that they will get at least one strike in 4 attempts (Hint 1 – P(no strikes) )
P(NONE)=
binompdf(4,0.7, 0) = 0.0081
P(at least one) = 1 – 0.0081 = 0.99
11. Jack and Jill play tennis. The probability of Jill winning is 0.55. What is the
probability that Jill will win at least one game out of a 5 game match?
(Hint 1 – P(no strikes) )
P(NONE)=
binompdf(5,0.55, 0) = 0.018
P(at least one) = 1 – 0.018 = 0.98
12. A four sided dice numbered 1, 2, 3, and 4 is rolled. What is the probability that
a 2 will be rolled at least once out of 6 rolls?
P(NONE)=
binompdf(6, (1/4), 0) = 0.18
p(at least one) = 1 – 0.18 = 0.82
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