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____ Suppose that
X followed the following theoretical distributions. Set up each distribution using the appropriate information from your data.
____ Uniform:
X ~
U ____________ Use the lowest and highest values as
a and
b .
____ Normal:
X ~
N ____________ Use
to estimate for
μ and
s to estimate for
σ .
____
Must your data fit one of the above distributions? Explain why or why not.
____
Could the data fit two or three of the previous distributions (at the same time)? Explain.
____ Calculate the value
k (an
X value) that is 1.75 standard deviations above the sample mean.
k = _________ (rounded to two decimal places) Note:
k =
+ (1.75)
s
____ Determine the relative frequencies (
RF ) rounded to four decimal places.
You should have one page for the uniform distribution, one page for the exponential distribution, and one page for the normal distribution.
____ State the distribution:
X ~ _________
____ Draw a graph for each of the three theoretical distributions. Label the axes and mark them appropriately.
____ Find the following theoretical probabilities (rounded to four decimal places).
______ From your original data (before ordering), use a random number generator to pick 40 samples of size five. For each sample, calculate the average.
______ On a separate page, attached to the summary, include the 40 samples of size five, along with the 40 sample averages.
______ List the 40 averages in order from smallest to largest.
______ Define the random variable,
, in words.
= _______________
______ State the approximate theoretical distribution of
.
~ ______________
______ Base this on the mean and standard deviation from your original data.
______ Construct a histogram displaying your data. Use five to six intervals of equal width. Label and scale it.
Calculate the value
(an
value) that is 1.75 standard deviations above the sample mean.
= _____ (rounded to two decimal places)
Determine the relative frequencies (
RF ) rounded to four decimal places.
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