Download 1-Simulation - VOLUMES-COKE

Math 116 – Chapter 7 – Distribution of Sample Means
Name_________________________
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) What is the variable? Specify the characteristics of the distribution: shape, mean, standard deviation.
b) Find the theoretical probability that a can selected at random will have a VOLUME of at least 12.1 oz.
(this is the process learned in chapter 6)
 Show all steps
 Check with the calculator feature
c) Let’s simulate the experiment of selecting a can of 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). How many times did you obtain a number 12.1
or more? Use this result to find the experimental probability of selecting a can with at least 12.1 oz.
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.
Show organized and neat work below
2) ) 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.
We select a sample of 36 Coke cans and the mean volume of the 36 cans is 12.1 oz.
a) Give the shape, mean and standard deviation of the distribution of sample means for samples of size 36.
b) Find the theoretical probability that a sample of 36 cans will have a mean amount of at least 12.1 oz.
 Show all steps
 Check with the calculator feature
c) Simulate the experiment of selecting a 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 five times.
Do: RandNorm(mu, sigma,36) →L1:mean(L1). OR mean(randNorm(mu, sigma,36)
How many times did you obtain a sample mean of at least 12.1 oz?
d) Let’s collect class’ results to find the experimental probability that a sample of 36 cans will have a mean
amount of at least 12.1 oz. Use this result to find the experimental probability of selecting a can with at least
12.1 oz.
e) Interpret the results from part (b).
If the mean of the volumes of regular coke cans is 12 oz, in ______ out of _________ samples of size 36 we
may observe a mean of at least 12.1 oz.
Based on this probability we can say that this is a _____________ event. (Complete with one of the following choices)
Very likely
likely
unlikely
very unlikely
e) An actual sample of 36 Coke cans was selected and the observed sample mean was 12.1 oz. Is it reasonable
to believe that the cans are actually filled with a mean of 12.00 oz?
f) If the mean is not 12.00 oz. as displayed in the Coke cans, are consumers being cheated? Explain.
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