0.4 Group and partner projects  (Page 2/4)

Part ii: possible distributions

____ 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 $\overline{x}$ 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 = $\overline{x}$ + (1.75) s
____ Determine the relative frequencies ( RF ) rounded to four decimal places.

1. RF ( X < k ) = ______
2. RF ( X > k ) = ______
3. RF ( X = k ) = ______

____ 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).

1. P ( X < k ) = ______
2. P ( X > k ) = ______
3. P ( X = k ) = ______

Part iii: clt experiments

______ 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, $\overline{X}$ , in words. $\overline{X}$ = _______________
______ State the approximate theoretical distribution of $\overline{X}$ . $\overline{X}$ ~ ______________
______ 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 $\overline{k}$ (an $\overline{X}$ value) that is 1.75 standard deviations above the sample mean. $\overline{k}$ = _____ (rounded to two decimal places)
Determine the relative frequencies ( RF ) rounded to four decimal places.

1. RF ( $\overline{X}$ < $\overline{k}$ ) = _______
2. RF ( $\overline{X}$ > $\overline{k}$ ) = _______
3. RF ( $\overline{X}$ = $\overline{k}$ ) = _______

1. P ( $\overline{X}$ < $\overline{k}$ ) = _______
2. P ( $\overline{X}$ > $\overline{k}$ ) = _______
3. P ( $\overline{X}$ = $\overline{k}$ ) = _______