Download Ch. 7.2 - Volumes of Coke

Math 117 – Introduction to Chapter 7
Name_________________________
Let’s review finding probabilities in a normal distribution – Chapter 6
1) Assume that cans of Coke are filled so that the actual amounts have a mean of 12.00 oz and a standard
deviation of 0.11 oz. Assume the volumes of Coke cans is normally distributed.
a) Describe the distribution of the variable: What is the variable? Specify the characteristics of the
distribution: shape, mean, standard deviation.
Sketch normal curve, label the mean and one, two and three standard deviations from the mean.
b) Make a random selection and find the likelihood of the observed value of the variable.
Find the theoretical probability that a can selected at random will have a VOLUME of at least 12.1 oz.
 Label this sample statistic on the graph of part (a) and shade the required area. How does this value “fit”
on this distribution? Is it usual (within two standard deviations from the mean) or unusual (more than
two standard deviations from the mean)?

Show all steps to find the probability

Check with the calculator feature
d) Interpreting results from part (b): The likelihood of selecting at random a can with volume 12.1 or more is
___________. Since this probability is
more/less than or equal to 0.05 (circle one), it is usual/unusual (circle
one) for a can to have a volume of 12.1 oz. or more.
e) Simulation: Let’s simulate the experiment of selecting a can from a normal distribution with mean 12.0 oz
and standard deviation 0.11 oz. Use randNorm(mu, sigma). (This is in the MATH, PRB menu). Do this ten
times and record the obtained value each time (round to 3 decimal places).
(1) List here the obtained values (each of these represent the volume of the cans selected at random):
__________________________________________________________________
(2) How many cans in your sample have a volume of 12.1 or more? _________________
(3) Use this result to find the experimental probability of selecting a can with at least 12.1 oz.
The experimental probability is ____________________
d) This will be done in class: Let’s collect class’ results to find the experimental probability of selecting at
random one can that contains at least 12.1 oz.
Section 7.2 - Distribution of sample means for samples of size n (x-bar distribution)
2) Are coke cans actually filled with an average amount of 12 oz. as displayed in a can? It makes
sense to think that the volumes of Coke cans are normally distributed; we’ll assume that the
standard deviation is 0.11 oz. .
To test what is claimed on the Coke-cans we select a random sample of 36 cans from this population and
we observe that the mean volume of the 36 cans is 12.1 oz.
Let’s study the distribution of sample means for samples of size 36 and observe how this sample fits in
such a distribution.
a) Describe the sampling distribution: Give the shape, mean and standard deviation of the distribution of
sample means for samples of size 36. Sketch normal curve, label the mean and one, two and three standard
errors from the mean.
b) Find the likelihood of this sample statistic: Find the theoretical probability that a sample of 36 cans will
have a mean amount of at least 12.1 oz.
 Label this sample statistic on the graph of part (a) and shade the required area. How does this statistic
“fit” on the distribution graphed above? Is it usual or unusual: likely to observe or unlikely?

Show all steps to find the probability

Check with the calculator feature
c) Interpret results from part (b).
If the mean volume of regular coke cans is 12 oz, in ______ out of _________ samples of size 36 we may
observe a sample mean of at least 12.1 oz.
Based on this probability we can say that this is a _____________ event if the means of coke cans is 12 oz.
(Complete with one of the following choices)
Very likely
likely
unlikely
very unlikely
d) Infer: What may this result suggest about the mean volume of Coke cans? Is it reasonable to believe that the
cans are actually filled with a mean of 12.00 oz.?
e) If the mean is not 12.00 oz. as displayed in the Coke cans, are consumers being cheated? Explain.
f) Simulation: Simulate the experiment of selecting a random sample of size 36 from a population with a mean
of 12 oz. and a standard deviation of 0.11 oz. and finding the mean of the sample. Do this ten times.
Do: Mean(RandNorm(mu,sigma,36))
Key strokes: Mean is in 2nd STAT[LIST], arrow to MATH, select 3: Mean(
RandNorm( is in the MATH menu (left column of calculator), arrow to PRB, select RandNorm
List here the ten sample-means obtained: ____________________________________________________
How many times did you obtain a sample mean of at least 12.1 oz? ___________
What is the probability of obtaining a sample mean of 12.1 or higher? ________________
g) Let’s collect class’ results and find the experimental probability of selecting a can with at least 12.1 oz.