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ECON 230 Lab 5: Normal Distribution and Z-Scores, Lab Reports of Statistics

Loyola Marymount University (LMU)Statistics

A lab exercise from an economics course (econ 230) focused on understanding the normal distribution and working with z-scores. Students are required to calculate the mean and standard deviation of a dataset (v2) using excel, sort the data, find z-scores, and perform various probability calculations using the normal curve.

Typology: Lab Reports

Pre 2010

Uploaded on 08/16/2009

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koofers-user-em4 🇺🇸

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ECON 230
Lab 5
The goal of this lab is to learn to work with the normal distribution.
Use V2, your data about a player’s slugging percentage, as the variable x that you’re interested
in learning about.
MAKE SURE TO HAND IN THE ANSWER SHEET ONLY WHEN YOU HAND IN LAB 5!
(1 point) 1. Use Excel to compute the mean and standard deviation of V2. You already calculated
these values in Lab 2. As long as you got the mean and standard deviation correct on Lab
2, you could just copy down the numbers from Lab 2.
(2 points) 2. Sort the list of 40 data values from smallest to largest, using the Excel directions about
how to sort at the end of the next page. Write down the values on lines #5, #20, and #35.
Compute the corresponding z-scores by subtracting the mean from each x value and
dividing by the standard deviation. Round to two decimal places. Your table should like
the table below. Suppose that I have a sample of 40 players and the mean slugging
percentage is 0.416 and the standard deviation is .096. My table would look like:
Line Number x value (slugging
percentage)
z-score
5 L=0.289 –1.32
20 M=0.452 0.38
35 H=0.648 2.42
In the table above, L should be the fifth-lowest value in your data set, M is a value
near the middle of your data set, and H is the fifth-highest value in your data set.
For the rest of the lab, you will make the assumption that your data is approximately normally
distributed. For each of the following problems, assume that the mean and standard deviation
are the values you found in problem 1.
(3 points) 3. Using the mean and standard deviation from question 1, and using the formula
x z
, find the data value x that goes with the following z-scores
Use
x
(the mean you found in Problem 1) and
s
(the standard
deviation you found in Problem 1).
.
i.
2 50
.
z
ii.
3 20
.
z
iii.
0z
(2 points) 4. Sketch (by hand) a normal curve with your value for
x
(the mean you found in part 1) as
. Take the three values specified in question 3 above, and locate them on your x–axis.
Clearly label the x– axis as a player’s slugging percentage. Round the corresponding z-
scores (from 3 above) to two decimal places. Write the z-scores below the x-axis.
1
pf3
pf4
pf5

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Download ECON 230 Lab 5: Normal Distribution and Z-Scores and more Lab Reports Statistics in PDF only on Docsity!

Lab 5 The goal of this lab is to learn to work with the normal distribution. Use V 2 , your data about a player’s slugging percentage, as the variable x that you’re interested in learning about. MAKE SURE TO HAND IN THE ANSWER SHEET ONLY WHEN YOU HAND IN LAB 5! ( 1 point) 1. Use Excel to compute the mean and standard deviation of V 2. You already calculated these values in Lab 2. As long as you got the mean and standard deviation correct on Lab 2, you could just copy down the numbers from Lab 2. ( 2 points) 2. Sort the list of 40 data values from smallest to largest, using the Excel directions about how to sort at the end of the next page. Write down the values on lines #5, #20, and #35. Compute the corresponding z -scores by subtracting the mean from each x value and dividing by the standard deviation. Round to two decimal places. Your table should like the table below. Suppose that I have a sample of 40 players and the mean slugging percentage is 0.416 and the standard deviation is .096. My table would look like: Line Number x value (slugging percentage) z -score 5 L=0.289 –1. 32 20 M=0.452 0. 38 35 H=0.648 2. In the table above, L should be the fifth-lowest value in your data set, M is a value near the middle of your data set, and H is the fifth-highest value in your data set. For the rest of the lab, you will make the assumption that your data is approximately normally distributed. For each of the following problems, assume that the mean and standard deviation are the values you found in problem 1. (3 points) 3. Using the mean and standard deviation from question 1 , and using the formula x    z , find the data value x that goes with the following z -scores Use^ ^  x^ (the mean you found in Problem 1) and^ ^  s^ (the standard deviation you found in Problem 1). .

i. z  2 50. ii. z 3 20. iii. z  0

( 2 points) 4. Sketch (by hand) a normal curve with your value for x (the mean you found in part 1) as  (^). Take the three values specified in question 3 above, and locate them on your x– axis. Clearly label the x– axis as a player’s slugging percentage. Round the corresponding z- scores (from 3 above) to two decimal places. Write the z- scores below the x- axis.

Lab 5 (4 points) 5. Using the methods shown in class and using the values you found in problem 2 for L, M, and H, find the following probabilities. INCLUDE A SKETCH WITH EACH PROBLEM AND MAKE SURE TO GIVE THE NUMERICAL ANSWER BELOW EACH SKETCH. MAKE SURE TO USE YOUR VALUES OF L, M, AND H (AND NOT MINE FROM THE EXAMPLE ON THE PREVIOUS PAGE). a. P( x < L) b. P( M<x<H ) (4 points) 6. A) Sketch a normal curve using your value for^ ^. Shade the area where the lowest 20% of your values would be (using the normal curve). Indicate the value for x that is the 20th^ percentile in the space provided below the sketch. B) Sketch a normal curve using your value for^ ^. Shade the area where the highest 5% of your values would be (using the normal curve). Indicate the value for x that is the 95th^ percentile in the space provided below the sketch. Excel Directions To sort your data by a given column:

  1. Go to the pulldown menu and choose: Data: Sort
  2. Then select: Sort by: Column A (If you want to sort by column A). You will want to sort by the column that contains slugging percentage.

Lab 5 iii) Answer: _____________________

**4. Sketch:

a)** P( x < L) = __________

Lab 5 b) _P( M < x < H) = ____________ 6. a) 20% of my x -values are below the following value for x : ____________. b) 5% of my x -values are greater than the following value for x : _____________.