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The following examples will be used to illustrate the Central Limit
Theorem.
Each of the examples has two parts, (a) and (b).
In part
(a) of the two examples, we will sample just one item from the
population (n = 1).
So, in part (a) we are talking about a random
variable,
X
.
In part (b) of the two examples, we will draw a random
sample of size n
≥
30 and compute the mean of the sample, that is
X
.
Therefore, in part (b) we will are talking about a random variable,
X
.
131
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.
Suppose that the Palmetto
Urgent Care
Center advertises a mean
wait to be seen by a physician on weekday evenings of 45 minutes.
Suppose that the actual wait time is uniformly distributed between 0
and 90 minutes.
a.
You (unfortunately) had to go to the center one weekday evening
and you waited 55 minutes before being seen a physician.
What is
the probability of a single patient waiting 55 minutes or longer if
Palmetto UCC’s claims about waiting times are true?
b.
Suppose that an audit was conducted in which records for 36
people who went to the Palmetto UCC were randomly sampled and
the wait time for each recorded.
The mean waiting time for the 36,
X
, was 55 minutes.
What is the probability that a random sample of 36
patients would have a mean waiting time of 55 minutes or longer if
Palmetto UCC’s claims about waiting times are true?
132
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This note was uploaded on 06/06/2011 for the course MGSC 291 taught by Professor Rollins during the Fall '09 term at South Carolina.
 Fall '09
 Rollins

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