Eco 502 Exam 3
10 points each
1. A local electronics store would like to offer an extended warranty on the
products it sells, but it’s hoping not to end up repairing many items. That
way the extended warranty is pure profit! Brilliant! Suppose the average
electronic item lasts an average of 53.3 months before it needs repair. The
standard deviation is 2.3 months and the distribution is normal. If the
manufacturer offers a 12- month warranty, and the store sells a 3-year
extension for a hundred bucks or so, what percentage of items will they have
to repair under warranty? Assuming repair costs are usually small, does this
sound like a reasonable plan?
covered
Not Covered
48
53.3
They will only have to repair about 1% of the
devices under warranty. Looks like a good idea.
2. An orange juice producer buys oranges from a large orchard nearby. Last
year the average orange from the orchard contained 4.7 ounces of juice
with a standard deviation of .4 ounces. This year the oranges seem
“drier.” (That is a technical juice term for a fruit that has less juice in it.)
The orchard manager claims that there is no difference. To settle the
matter, the juicer samples 64 oranges and finds the average is 4.5 ounces.
While the sample average is obviously less than 4.7 ounces, the orchard
manager claims this is typical sample variation and does not indicate a
problem. Is he right? Explain your answer.
4.5
4.7
There is less than 1 percent chance that the average would be that low if the
population was 4.7. This does not seem to be normal sample variation. I’d
say the fruit is drier.
3. “If your clothes aren’t ready in two days the cleaning is free!” is the new
slogan for a local 24 hour dry cleaner. Clothes typically take 1.2 days to
clean with a standard deviation of .4 days. Based on this information, the
manager figures that they will only have to give the free cleaning to 2.28%
of the customers. After the first week he is surprised to find out that actually
5 percent of the customers are getting free cleaning. There are three
possible explanations for this. What are they?
Normal with description given above should result in 2.28% freebies so
either:
1. The mean has changed (perhaps his operation is slowing down.
2. There is more variance (his cleaning process is not as consistent.
3. The distribution is not normal.
4. (5 points) Without referencing a formula, explain why the standard error
of a sampling distribution gets smaller as the sample size increases.
As the sample size increases, the sample average more accurately reflects
the true average, so there is less variance in the sample averages and a
smaller standard error.
5. (5 points) Explain why is it usually better to use a sample size larger than
30? If the population is normal, any sample will yield usable results.
However if the population is not normal, the sample averages will be normal
so long as the sample size is over 30.