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Probability Distributions - Discrete
No Data Set Needed
1. In each part, indicate, (1) whether the variable is discrete or continuous AND (2) whether it is
binomial or not AND (3) if it is binomial, give values for n and p.
a. Number of times a “head” comes up in 10 flips of a coin
1. Discrete or continuous
2. Binomial yes or no
3. If Binomial what is n and p?
b. Time to complete a 30 question multiple choice test
1. Discrete or continuous
2. Binomial yes or no
3. If Binomial what is n and p?
c. Number of correct answers on a 30 question multiple choice test for somebody who randomly
guesses at every question. There are four answer choices for each question,
1. Discrete or continuous
2. Binomial yes or no
3. If Binomial what is n and p?
d. A woman buys a lottery ticket every week for which the probability of winning anything at all
is 1/10. She continues to buy them until she has won 3 times. X = the number of tickets she buys.
1. Discrete or continuous
2. Binomial yes or no
3. If Binomial what is n and p?
2. From a survey the following table gives the number of classes student’s reported missing
during the semester (represented by X) and the probability for each of these X values.
X = missed classes
P(X = x)
0
1
2
3
4
5
6
7
8
0.56
0.23
0.13
0.03
0.02
0.01
???
0.01
0.01
a. Is X = missed days discrete variable or a continuous variable? Explain.
b. What must be the value of the probability for X = 6 and how did you calculate that probability?
c. Determine E(X), the mean number of missed days and provide an interpretation of this value.
d. Find the probability that the number of missed days is 3 or less.
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e. When we find the probability that a discrete variable is less than or equal to some value it is
called a cumulative probability. To find it, we add probabilities for all values up to and including
that point. For each number of missed days determine the cumulative probability.
X = missed classes
0
1
2
3
4
5
6
7
8
Cumulative prob.
f. Use the cumulative probabilities just found as an aid in finding the probability that the number
of missed days for a randomly selected student would be greater than 4. Show work.
BINOMIAL RANDOM VARIABLE SECTION
3. Suppose somebody randomly guesses at every one of 10 True-False questions.
a. The number of correct guesses is a binomial random variable. What are the values of the
parameters n and p?
n=
p=
b. What is the expected number and standard deviation of correct guesses of the n = 10
questions? Show how you determined this.
USE MINITAB FOR THE REMAINING QUESTIONS - Instructions on how to use
Minitab to calculate binomial probabilities to answer the following can be found in the
online notes for this lesson by clicking the tab: Binomial Random Variable.
c. Assuming random guessing, what is the probability that the number of correct guesses is 6 or
fewer?
d. What is the probability that somebody just guessing could get 7 or more correct? Show work
(Hint: This is the complement of the previous part.)
e. What is the probability that somebody just guessing would get 9 or more correct? (Hint: You’ll
have to deal with the probability of 8 or less first).
f. What is the probability that somebody just guessing gets exactly 5 correct? (You’ll have to
click on Probability rather than Cumulative Probability in the Minitab dialog box.)
g. What is the probability that the number correct for somebody just guessing is one of 8, 9, or 10
correct? Hint: First find separate probabilities for each of 8, 9, and 10. Show any work.
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