devry math221n week 4 ilab latest 2015 october

Statistics – Lab Week 4

Name:_______________________
MATH221

Statistical Concepts:
·
Probability
·
Binomial Probability Distribution

Calculating Binomial
Probabilities

Ø Open a new MINITAB worksheet.

Ø We are interested in a binomial experiment with 10 trials. First, we
will make the probability of a success ¼. Use MINITAB to calculate the
probabilities for this distribution. In column C1 enter the word ‘success’ as
the variable name (in the shaded cell above row 1. Now in that same column,
enter the numbers zero through ten to represent all possibilities for the
number of successes. These numbers will end up in rows 1 through 11 in that
first column. In column C2 enter the
words ‘one fourth’ as the variable name. Pull up Calc > Probability Distributions > Binomial and select the
radio button that corresponds to Probability.
Enter 10 for the Number of trials:
and enter 0.25 for the Event
probability:. For the Input column:
select ‘success’ and for the Optional
storage: select ‘one fourth’. Click the button OK and the probabilities will be displayed in the Worksheet.

Ø Now we will change the probability of a success to ½. In column C3
enter the words ‘one half’ as the variable name. Use similar steps to that
given above in order to calculate the probabilities for this column. The only difference is in Event probability: use 0.5.

Ø Finally, we will change the probability of a success to ¾. In column
C4 enter the words ‘three fourths’ as the variable name. Again, use similar steps to that given above
in order to calculate the probabilities for this column. The only difference is
in Event probability: use 0.75.

Plotting
the Binomial Probabilities

1.
Create plots for the three
binomial distributions above. Select Graph
> Scatter Plot and Simple
then for graph 1 set Y equal to ‘one fourth’ and X to ‘success’ by clicking on
the variable name and using the “select” button below the list of
variables. Do this two more times and
for graph 2 set Y equal to ‘one half’ and X to ‘success’, and for graph 3 set Y
equal to ‘three fourths’ and X to ‘success’.
Paste those three scatter plots below.

Calculating Descriptive
Statistics

Ø Open the class
survey results that were entered into the MINITAB worksheet.

2.
Calculate descriptive statistics for the variable
where students flipped a coin 10 times. Pull up Stat > Basic Statistics > Display Descriptive Statistics and
set Variables: to the coin. The
output will show up in your Session Window.
Type the mean and the standard deviation here.

Mean:

Standard deviation:

Short Answer Writing
Assignment – Both the calculated binomial probabilities and the descriptive
statistics from the class database will be used to answer the following
questions.

3.
List the probability value for each possibility in
the binomial experiment that was calculated in MINITAB with the probability of
a success being ½. (Complete sentence not necessary)

P(x=0)

P(x=6)

P(x=1)

P(x=7)

P(x=2)

P(x=8)

P(x=3)

P(x=9)

P(x=4)

P(x=10)

P(x=5)

4. Give the
probability for the following based on the MINITAB calculations with the
probability of a success being ½. (Complete sentence not necessary)

P(x?1)

P(x<0) P(x>1)

P(x?4)

P(4

Mean:

Standard deviation:

6. Calculate the
mean and standard deviation (by hand) for the MINITAB created binomial
distribution with the probability of a success being ¼ and compare to the
results from question 5. Mean = np,
Standard Deviation = .gif”>

Mean:

Standard deviation:

Comparison:

7. Calculate the
mean and standard deviation (by hand) for the MINITAB created binomial
distribution with the probability of a success being ¾ and compare to the
results from question 6. Mean = np,
Standard Deviation = .gif”>

8. Explain why the
coin variable from the class survey represents a binomial distribution.

9. Give the mean and
standard deviation for the coin variable and compare these to the mean and standard
deviation for the binomial distribution that was calculated in question 5.
Explain how they are related. Mean = np,
Standard Deviation = .gif”>