Download Lab #3

STATISTICS – LAB #3
Statistical Concepts
 Normal Probability Distribution
 Empirical Rule
Calculating Normal Probabilities
 Open a new MINITAB worksheet.
 The amount of TV the average person watches per day has a normal distribution
with a mean of 4.7 hours and a standard deviation of 1.3. Use MINITAB to
calculate all of the probabilities asked for in questions 1 and 3. To calculate
probabilities in the software, pull up Calc > Probability Distributions >
Normal. If you are not finding probabilities for the standard normal distribution
then enter the Mean: and Standard deviation: for the distribution. Select the
radio button corresponding to Input constant: and input the value for which
you are finding the probability. Also, select Cumulative probability if you are
interested of being less than or equal to some value, and select Inverse
cumulative probability if you are trying to find a critical value. For example if
you want to find P( z  1) for the standard normal distribution, then input 1 for
the Input constant: and select Cumulative probability. You should get
0.8413 as your answer.
Calculating Descriptive Statistics
 Open the class survey results that were entered into the MINITAB worksheet.
 Calculate descriptive statistics for the variable from the survey that asks how
long do you watch TV each day. Pull up Stat > Basic Statistics > Display
Descriptive Statistics and set Variables: to TV. The output will show up in
your Session Window. Print the Session Window that should display all
calculations necessary to answer the questions.
Create a Histogram
 Create a histogram for the variable TV – Pull up Graph > Histogram and
select With Fit and click OK. Set Graph variables: equal to TV. Title the
graph (put your name in as the title). Now print the graph.
Short Answer Writing Assignment
Include copies of all print outs with this assignment.
1. Sketch the density curve, with the values for each situation. Then, solve each of
the following for the standard normal distribution using MINITAB.
a. P(z  1.64) 
b. P(z  .46) 
c. P(1.24  z  2.13) 
2. Explain the characteristics of the normal distribution. Is there any reason to
think that the distribution of TV watching time is not normal? Explain using the
histogram as support for your comments.
3. Sketch the density curve for each situation and explain the answer in the context
of the problem. Given the mean (4.7 hours) and standard deviation (1.3 hours)
for the population of TV watching, find the following:
a. What proportion of people watch TV more than 6 hours a day?
b. What proportion of people watch TV between 4 to 7 hours?
c. Ninety-five percent of people watch TV less than how many hours?
4. Give the mean and standard deviation for TV watching from the survey data
and compare these to those of the population. Explain similarities and/or
differences and describe why this is possible.
5. Give the range of the data for the TV watching variable for this class. Use the
range to estimate the standard deviation for this data (think about the empirical
rule). Explain your approach for this estimation.
6. Is the estimate in question 5 a good estimate for the standard deviation? Explain
your reasoning.