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

* Find Probabilities for specific Normal Distributions

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:

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

* Find Probabilities for specific Normal Distributions

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?

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. )

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.

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.

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%?___________________