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One major oversight of our excitement with this idea is the notion that we would actually know
the true population mean, , and the true population standard deviation, . If we have limited
information about our population, then we certainly would not know these values. In the next
parts of this chapter, we will learn how to use our sample to make these predictions about the
population. Though similar in conceptual nature, it is not as straightforward as replacing with ̅
and with .
Homework Problems – 6.1
1. In your own words, what does the Central Limit Theorem tell us
2. In your own words, why is the Central Limit Theorem a very powerful practical result
3. A sample of size 36 is taken from a population distribution of unknown shape, though the
mean is believed to be 100 with a standard deviation of 18. What is the probability that
the sample mean is:
a. Greater than 102
b. Less than 98
c. Between 95 and 105
d. Between what two values will the middle 90% of means be
4. A stained glass company produces panes of glass with a mean thickness of 0.42 inches
and a standard deviation of 0.04 inches, if produced properly. Suppose a random sample
of windows reveals a sample mean of 0.43.
a. What is the probability of this average, or a larger average
b. Given the probability you have computed, what can be said about recent
production standards
5. Promote Marketing has a research team to research new marketing tactics to propose to
potential clients. A group of 40 clients have been invited for a conference to be put on by
the marketing firm. The research team usually generates
in revenues for
each member of the team with .
a. What will be the shape of the distribution of ̅ How do you know
b. What is the probability that average sales will exceed $420,000 for this particular
event
c. How would your answer change if 100 clients were to show up
d. If the team (300 people) have an average revenue that is in the 90 th percentile of
revenues, they will earn 4-days of paid vacation. What average sales would be
required for this
6. A computer simulation reveals that a distribution of average incomes in a sample of 500
has a standard deviation of $130. What is the standard deviation for the population of all
incomes Interpret the result you get in real-world terms.
7. Use the Excel Sampling Distribution Applet to address this problem. In a population, it is
found that 30% of homes have 5 rooms, 40% have 4 rooms, and 30% have 3 rooms. You
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