# 6.9 Normal distribution: normal distribution lab i (edited: teegarden

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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.

${\overline{x}}_{1}$ = _________ ${\overline{x}}_{2}$ = _________ ${\overline{x}}_{3}$ = _________ ${\overline{x}}_{4}$ = _________

${\overline{x}}_{5}$ = _________ ${\overline{x}}_{6}$ = _________ ${\overline{x}}_{7}$ = _________ ${\overline{x}}_{8}$ = _________

${\overline{x}}_{9}$ = _________ ${\overline{x}}_{10}$ = _________

## 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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