Math 160: Lab 2 – The Normal Distribution – Due on Exam Day
You wil ned to copy, paste and edit your resulting graphs and tables on to an answer document
as you complete each question. Your answers must be submited in a word document of
your choice (WORD, Google DOC, etc), no answers should be hand writen. Include the
question with your answers.
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Problem 1:
It is generaly accepted that the mean body temperature is 98.6 degrees.
If a sample of size 10 resulted in a sample mean of 98.3 degrees with a
standard deviation of 0.64 degrees. Does this sample sugest that the
mean body temperature is actualy lower than 98.6 degrees?
You wil be answering this question by completing a simulation on
StatCrunch.
Go to ww.StatCrunch.com ( using your MyStatLab user Id and PW)
Select OPEN StatCrunch
Using your StatCrunch menu select Data -> Simulate Data-> Normal
You ned to generate 10 values from a normaly distributed population with a
mean of 98.6 degres and a standard deviation of 0.64 degres (using the sample
standard deviation given in the situation since the population deviation is
unknown). To repeat the simulation 9 more times for a total of 10. (input 10
row and 10 columns)
This wil give you the folowing window… EVERYONE wil get diferent results.
However you should have 10 columns each with 10 values.
Use Stat -> Summary Stats -> Column and select al 10 columns to determine the
sample mean for each data set. To select the columns, click on the first one (
Normal1) then scrol down to the last one ( Normal10) Hold down the SHIFT key
and click on Normal10. This should select al columns.
Question 1: Paste your answers into your answer document
1a) COPY the Sumary stats table into your answer document .
1b) Record the values of
, , , , , , , , , and into your answer document .
1c) Now find = ________
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Problem 2: Finding Probabilities for
Normal Distribution
For each of the folowing distributions, answer the folowing:
First: write the question in symbolic form, then
Second: use StatCrunch to find the probabilities (Stat -> Calculator -> Normal),
Third: Copy the StatCrunch graph to each situation .
Example:
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
0.894 ( notice that StatCrunch only has the or symbol)
Question 1: Paste your answers into your answer document
Analyze the Data – Using complete sentences.
1d) Based on your simulation, do you think that ONE sample of size 10 with a mean
temperature of 98.3 and standard deviation of 0.64 sugest that the mean body temperature is
actually lower than 98.6 degres?
1e) Can the mean from one sample target the population mean?
1f) Can the mean from al sample means ( ) target the population mean?
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For each of the folowing distributions, answer the folowing:
First: write the question in symbolic form, then
Second: use StatCrunch to find the probabilities (Stat -> Calculator -> Normal),
Third: Copy the StatCrunch graph to each situation .
Question 2: Paste your answers into your answer document
a.) 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.
b.) Given a population with a normal distribution, a mean of 10, and a standard deviation
of 20, find the probability of a value between 87 and 122.
c.) 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?
d.) 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?
e.) 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?
f.) Given a population with a normal distribution, a mean of 20, and a standard deviation of
15, which two values form. the uper and lower boundary of the midle 80%?
Upper:
Lower:
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Problem 3: OBTAINING CONFIDENCE INTERVALS
You have a random sample of 106 body temperatures that
have a mean of 98.2 degres Faharenheit and a standard
deviation of 0.62 degres Faharenheit. Construct a 95%
confidence interval estimate of the mean body
temperature of the entire population.
MEANS:
Open a blank spreadshet in Statcrunch.
Click on STAT, then Z STATISTICS OR T STATISTICS
Then select ONE SAMPLE OR TWO SAMPLE
Then select whether you wil be using raw data (a column of values) or
sumarized data
Once you do this (selecting “with sumary” for entering statistics instead of
raw data), Statcrunch wil automaticaly open the folowing:
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After entering the sumary statistics, you wil then ned to click on NEXT so
that you obtain the following:
It is here that you wil select CONFIDENCE INTERVAL. The default
confidence level is .95, but that can easily be changed.
Click CALCULATE. You wil see something like this:
*Note that a similar procedure would produce similar results when selecting
T STATISTICS instead of Z STATISTICS.
*Note that two sample procedures folow the same general procedure, but of
course require two sets of sample statistics
Question 3: Paste your answers into your answer document
a) What is the 95% confidence interval?
b) Interpret the confidence interval
c) What does this confidence interval sugest about the comon belief that 98.6
degrees Faharenheit is the mean body temperature?