Lab 4 Jake Keppler
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Mathematics
Date
Jan 9, 2024
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MATH 131
1/2021
Lab 4
Jake Keppler
The goal of this lab is to define a binomial experiment and find binomial probabilities by two different methods.
(2 points) Part
1:
Experiment
Definition
A.
Return to Lab 2, V1
. Define “success” for your qualitative data to be the category with the largest relative frequency from your Lab 2 Part 1A table. Batting left has the largest relative frequency from Lab 2 V1
B.
Name what a failure will be for your qualitative data. Batting with both hands (If you have more than one category, combine and name them as “Others”)
C.
What is your value for p
, the probability of success from A? .475
D.
What is your value for q
? .525
You
will
not
actually
be
collecting
any
new
data
for
Parts
2
and
3.
You
will
be
finding
probabilities associated with specific numbers of trials of the experiment stated.
(4 points) Part
2:
Binomial
Formula
(n=3)
A.
Using the correct formula and showing
your
calculations
,
create a table as noted here for three independent trials. ( x is the number of successes in 3 trials.) 0 ≤ x ≤ 3
. Calculations: XX
P(X)
1
0.1447
2
0.3928
3
0.3554
4
0.1072
B.
What are the two criteria for a valid probability distribution? Use them to verify that
your probability distribution from part A is valid. Check the sum of your own probabilities.
(1)
The sum of all probabilities equals 1 and every probability is between 0 and 1.
(2)
MATH 131
1/2021
Lab 4
C.
Find the mean of the probability distribution from part A using two
different
methods
(one from Section 5.1 and one from Section 5.3). Show your work. (1)
3*0.475=1.425
0*0.1447+1*.3928+2*.3554+3*.1072=1.425
(2)
MATH 131
1/2021
Lab 4
(4 points) Part
3:
Binomial
Table
or
Computer
(n=10)
A.
Using the binomial table in your text or
the computer (See computer notes below),
create a table similar to Part 2 but for n = 10 trials. 𝑥𝑥 is number of successes.
𝑥𝑥
𝑃𝑃
(
𝑥𝑥
)
0
.0016
1
.0144
2
.0586
3
.1414
4
.2238
5
.2430
6
.1832
7
.0947
8
.0321
9
.0065
10
.0006
B.
Using the table above to answer the following. For parts 2-4, show the individual
values
that
you
are
adding
up,
as
well
as
the
total.
The
answer
alone
is
not
sufficient
(1)
What is the probability of exactly 10 successes? 0.0006
(2)
What is the probability of no more than 3 successes? P(x=0)+P(x=1)+P(x=2)+P(x=3)
.0016+.0144+.0586+.1414
=.2160
(3)
What is the probability of at least 7 successes? P(x=7)+P(x=8)+P(x=9)+P(x=10)
.0947+.0321+.0065+.0006
=.1339
(4)
What is the probability of between 2 and 9 successes (inclusive)? 1-
(P(x=0)+P(x=1)+P(x=10))
1-(.0016+0.0144+.0006)
=.9834
Excel
Minitab
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MATH 131
1/2021
Lab 4
For calculating probability of exactly 𝒙𝒙 successes in n trials with P(success) = p
.
=BINOM.DIST(
x, n, p
, FALSE)
Repeat for each value of x
between 0 and n.
•
Type the x values (0 – 10) in C
1
.
•
Select Calc
Probability Distribution
Binomial
Choose Probability
•
Enter Number of Trials and the Probability of Success for
your data
•
Tell Minitab that the x values are in C1 and that you want
the probabilities stored in C2 by entering C1 as the Input
Column and C2 for Optional Storage