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Normal Distribution: Normal Distribution Lab I (edited: Teegarden)

Module by: Mary Teegarden. E-mail the author

Based on: Normal Distribution: Normal Distribution Lab I by Barbara Illowsky, Ph.D., Susan Dean

Summary: Labs changed to incorporate mini-tabs.

Normal Distribution Lab

Name:

I Student Learning Outcome:

* The student will compare and contrast empirical data and a theoretical distribution.

* Find Probabilities for specific Normal Distributions

II The Situation

It is generally accepted that the mean body temperature is 98.6 degrees. If a sample of size 100 resulted in a sample mean of 98.3 degrees with a standard deviation of 0.64 degrees. Does this sample suggest that the mean body temperature is actually lower than 98.6 degrees?

III Simulation: To answer the question, complete the following simulation.

Using Minitab (Calc -> Random Data-> Normal), generate 100 values from a normally distributed population with a mean of 98.6 degrees and a standard deviation of 0.64 degrees (using the sample standard deviation given in the situation since the population deviation is unknown). Repeat the simulation 9 more times for a total of 10. (Requesting the data be stored in c2-c10 will generate the remaining 9 columns of data with one command. )

IV Data Collection

Use Stats -> Basic Stats -> Display Descriptive and select all 10 columns to determine the sample mean for each data set. Record the values below and include the session window with this lab.

x¯1x¯1 size 12{ {overline {x}} rSub { size 8{1} } } {} = _________ x¯2x¯2 size 12{ {overline {x}} rSub { size 8{2} } } {} = _________ x¯3x¯3 size 12{ {overline {x}} rSub { size 8{3} } } {} = _________ x¯4x¯4 size 12{ {overline {x}} rSub { size 8{4} } } {} = _________

x¯5x¯5 size 12{ {overline {x}} rSub { size 8{1} } } {} = _________ x¯6x¯6 size 12{ {overline {x}} rSub { size 8{2} } } {} = _________ x¯7x¯7 size 12{ {overline {x}} rSub { size 8{3} } } {} = _________ x¯8x¯8 size 12{ {overline {x}} rSub { size 8{4} } } {} = _________

x¯9x¯9 size 12{ {overline {x}} rSub { size 8{1} } } {} = _________ x¯10x¯10 size 12{ {overline {x}} rSub { size 8{2} } } {} = _________

V Analyze the Data – Using complete sentences.

Based on your simulation, do you think that a sample of size 100 with a mean temperature of 98.3 is reasonable? Answer using 2 – 3 complete sentences.

VI Finding Probabilities for Normal Distribution

For each of the following, first write the question in symbolic form and then using Minitab (Calc -> Probability Distributions -> Normal), find the probabilities. (attach your session window to this lab)_____________________

1. Given a population with a normal distribution, a mean of 0, and a standard deviation of 1, find the probability of a value less than 1.25 _____________________

2. Given a population with a normal distribution, a mean of 25, and a standard deviation of 3, find the probability of a value greater than 21.25._____________________

3. Given a population with a normal distribution, a mean of 100, and a standard deviation of 20, find the probability of a value between 87 and 122._____________________

4. Given a population with a normal distribution, a mean of 150, and a standard deviation of 35, what value has an area of 0.34 to the left?_____________________

5. Given a population with a normal distribution, a mean of 150, and a standard deviation of 35, what value has an area of 0.34 to the right?_____________________

6. Given a population with a normal distribution, a mean of 15, and a standard deviation of 2, what value has an area of 0.8 to the left?_____________________

7. Given a population with a normal distribution, a mean of 200, and a standard deviation of 15, which two values form the upper and lower boundary of the middle 80%?___________________

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