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There are three problems. You are to do the work on this assignment! You may talk with others
about it or how they think a particular part should be done, but when you submit your responses
you are presenting your work and not that of someone else. Hence you may consult with
consultants on what should be done but you can not use any subcontractors for the work.
1. Get a coffee mug, tea cup or similar cylindrical container and a small object such as a penny.
Place the container on a table and stand far enough away from the container so that your arm
when extended is about a meter from the cup. You are to toss the object at the cup trying to
place it in the cup. Alternate for each trial between your right and left hand and toss the coin 20
times with each hand for a total of 40 times.
a. Record the results in the table below and use this information to determine each of the
requested probabilities or to answer the question asked. If the object hits in the container
but rebounds out then it is not recorded as being in the cup.
Left Hand
Right Hand
Total
In the container
Not in the container
Total
20
20
40
b. Find the marginal probability of the object being in the container.
c. Find the probability of the object being in the container if you used your left hand.
d. Find the probability of the object being in the container if you used your right hand.
e. Do you think the probability of you tossing the object into the container is independent of
the hand you use? Give a reason for your conclusion.
f. Suppose you toss a coin to determine which hand you will use to toss the object and you
will use your left hand to toss the object at the container if the coin is tails and the right hand
if the coin is heads. Hence you are as likely to use your right hand as you are to use your
left hand. I walk into the room after you have tossed the object and observe that the object
is not in the container. What is the probability that you tossed the object with your left
hand?
2. Identify a variable (measurement) from a work context that you think could reasonably be
modeled by a binomial distribution.
a. Provide an explanation of why you think this variable could reasonably be described by a
binomial distribution.
b. Give numerical values for the parameters of this binomial distribution if you observe 25
individual trials and tell how you arrived at these particular values for the parameters.
c. Understanding that the values for the variable in a binomial distribution are integers, find
the integer value for the variable that would have the cumulative probability that is closest
to 5%. Now find the integer value for the variable that would have the cumulative
probability that is closest to 95%.
d. Average the two values you found in part c and round the answer up to the nearest integer
value and use the binomial to find the probability of observing a numerical value for this
variable that is at least as large as this rounded average value.
3. Identify a variable (measurement) from a work context that you think could potentially be
modeled by a normal distribution.
a. Provide an explanation of why you think this variable could reasonably be described by a
normal distribution.
b. Subjectively assess or if you have actual data use it to estimate the values of the 5th
percentile, median and 95th percentile for the distribution of these values.
c. The extended Pearson-Tukey method represents a continuous distribution with a 3-point
discrete distribution that assigns probabilities to the values for 5th percentile, median and
95th percentile, with the 5th and 95th percentile each being assigned a probability of .185 and
the median is assigned a probability of .63. These probabilities are assigned to the values
you have determined for the 5th percentile, median and 95th percentile in the table below.
X (your estimate)
P(X)
X•P(X)
(X-)
(X-)2•P(X)
5th percentile
.185
median
.63
95th percentile
.185
d.
Using this information find the expected value, E(X), which is the mean of the distribution,
and the variance of the distribution, 2. Find the square root of the variance to determine the
standard deviation, .
Use the values for the mean  and the standard deviation  from above as the parameters of
a normal distribution. Find the 5th percentile value for a normal distribution with the above
specified parameters, that is the value for which the cumulative probability is .05. (This can
be accomplished using the NORMINV function in Excel or using the method for finding x.05
on pages 182 and 183 of the Canavos and Miller text. Similarly find the 95th percentile
value for this normal distribution which is x.95 as illustrated on page 184 of the Canavos and
Miller text.
My website URL is http://www.people.vcu.edu/~randrews/
From this page there is a link to the lecture materials that sends you to
http://www.people.vcu.edu/~randrews/c-m99/c-m99info.html and you can go to
the page with excel files with my solutions to selected problems from the text at
http://www.people.vcu.edu/~randrews/c-m99/c-m99hw.html