No.
Since the original population was normal, the mean is exactly normal for any
n
.
3. The waiting time for a rollercoaster ride follows a skewed distribution with a standard
deviation of 1 minute.
(a)
Suppose the average wait time in a sample of 50 people is 5 minutes.
Estimate the
average wait time for all riders.
We can use the CLT to say that
X
is approximately normal, with mean
5
=
=
X
X
μ
μ
and standard
deviation
50
1
=
=
n
X
X
σ
σ
.
“Estimate the average wait time for all riders” means find a 95% confidence
interval for
μ
.
The interval is:
=
±
=
±
=
±
277
.
0
5
50
1
96
.
1
5
96
.
1
n
X
X
σ
(4.723, 5.277)
4. Suppose the number of channels in a subscriber’s cable package has a normal distribution,
with mean 80 and standard deviation 10.
(a)
If 100 subscribers are chosen at random, what is the probability that the average number
of channels in their cable packages is larger than 79.5?
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We want
)
5
.
79
(
X
P
.
We can compute
5
.
0
100
10
80
5
.
79

=

=
=
=
n
X
Z
X
X
σ
μ
.
Thus
)
5
.
0
(
)
5
.
79
(

=
Z
P
X
P
.
From the normal tables, this probability is 1 – 0.3085 = 0.6915.
(b)
Did you use the CLT to answer part a?
Why/why not?
No. Since the original population is normal,
X
is exactly normal.
5. In the 1970s, the average age of a baseball player was estimated to be 32 years old, with a
standard deviation of 3 years.
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 Winter '12
 Johnson
 Statistics, Normal Distribution, Standard Deviation

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