# A) Write a brief definition of the word quartile as we have used

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a) Write a brief definition of the word \"quartile\" as we
have used it in previous weeks.
_____________________________.
b) Write a brief definition of the word \"quantile\" as it
might be used in statistics.
________________________________.
c) From within interactive R, enter the command shown
below (the command shows a help page for the pbinom
command). Provide a very brief description of the
arguments that are passed to the pbinom() command
(\"arguments\" in computer programming are the options
that you give to a function so that the function can
calculate what you want it to). Note that one of the
arguments is lower.tail = TRUE, and because there is a
value assigned to it with the equals sign, it means that if
you do not enter a new value for lower.tail, it will be set to
TRUE by default. Do not type the \">\" into R, it is the
command prompt:
> ?pbinom
2) You can use the dbinom() command (function) in R to
determine the probability of getting 0 heads when you flip
a fair coin four times (the probability of getting heads is
0.5):
dbinom(0, size=4, prob=0.5)
Find the equivalent values for getting 1, 2, 3, or 4 heads
when you flip the coin four times. TIP: after you run the
first dbinom() command, press the up arrow and make a
small change and run it again.
probability of getting exactly 1 head: _______
probability of getting exactly 2 heads: _______
probability of getting exactly 3 heads: _______
probability of getting exactly 4 heads: _______
3) Use the pbinom() function in R to show the cumulative
probability of getting 0, 1, 2, 3, or 4 heads when you flip
the coin 4 times (this is the same as finding the probability

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than the value is less than or equal to 0, 1, 2, 3, or 4.)
probability of getting no more than 0 heads: ____
probability of getting no more than 1 head: _____
probability of getting no more than 2 heads:_____
probability of getting no more than 3 heads: ____
probability of getting no more than 4 heads: ____
4) The following R command will show the probability of
exactly 6 successes in an experiment that has 10 trials in
which the probability of success for each trial is 0.5:
dbinom(6, size=10, prob=0.5)
(True/False)____________
5) Read Yakir (2011, pp. 68-69) carefully to review the
meaning of the pbinom function (related to tests that a
value will be equal to versus less than or equal to a
criterion value). What is the probability of getting fewer
than 2 heads when you flip a fair coin 3 times (round to 2
decimal places) ? ______
6) What is the probability of getting no more than 3 heads
when you flip a fair coin 5 times (be sure to understand the
wording differences between this question and the
previous oneround to 2 decimal places)? ________
---------------------------------------------------
Information
The exponential distribution is a continuous distribution.
The main R functions that we will use for the exponential
distribution are pexp() and qexp(). Here is an example of
the pexp() function. Leaves are falling from a tree at a rate
of 10 leaves per minute. The rate is 10, or we can say that
lambda = 10 (meaning 10 leaves fall per minute). The
leaves do not fall like clockwork, so the time between
leaves falling varies. If the time between leaves falling can
be modeled with an exponential distribution, then the
probability that the time between leaves falling will be less
than 5 seconds (which is 5/60 of a minute) would be:
(note: this is an explanation of how pexp() works, you will

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a) Write a brief definition of the word \"quartile\" as we have used it in previous weeks. _____________________________. b) Write a brief definition of the word \"quantile\" as it might be used in statistics. ________________________________. c) From within interactive R, enter the command shown below (the command shows a help page for the pbinom command). Provide a very brief description of the arguments that are passed to the pbinom() command (\"arguments\" in computer programming are the options that you give to a function so that the function can calculate what you want it to). Note that one of the arguments is lower.tail = TRUE, and because there is a value assigned to it with the equals sign, it means that if you do not enter a new value for lower.tail, it will be set to TRUE by default. Do not type the \">\" into R, it is the command prompt: > ?pbinom 2) You can use the dbinom() command (function) in R to determine the probability of getting 0 heads when y ou flip a fair coin four times (the probability of getting heads is 0.5): dbinom(0, size=4, prob=0.5) Find the equivalent values for getting 1, 2, 3, or 4 heads when you flip the coin four times. TIP: after you run the first dbinom() command, press the up arrow and make a small change and run it again. probability of getting exactly 1 head: _______ probability of getting exactly 2 heads: _______ probability of getting exactly 3 heads: _______ probability of getting exactly 4 heads: _______ 3) Use the pbinom() functi ...
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