190
CHAPTER
4
Statistical Sampling
(d)
K11allenge) The company's
primary
concern is to avoid underestimating
the av
erage amount
claimed by its policyholders.
Determine
a value
b
so that the in
surance
company
is 95% confident
that
the
average
amount
claimed
by its
policyholders
is
b
or less.
EXERCISE 4.3 According
to annual
precipitation
data kept for the past 75 years,
the average
precipitation
in New York City is 41.76 inches per year and
the ob
served sample
standard
deviation
is 5.74 inches per year.
(a)
Construct
a 99% confidence
interval
for the mean of the distribution
of yearly
precipitation
in New York City.
(b) Determine the required sample size in order to estimate the mean of the distrib
ution of yearly precipitation
in New York City to within
1.2 inches at the 99%
confidence level.
(c)
During the same 75year period,
the average precipitation
in Tokyo was 34.37
inches per year and the observed sample standard
deviation was 4.98 inches per
year. Construct
a 95% confidence
interval for the difference between
the mean
yearly precipitation
in New York and Tokyo.
EXERCISE 4.4A company manufacturing
stereo equipment
claims that their personal
CD player can be used for approximately
8 hours of continuous
play when used with
alkaline batteries. To provide this estimate, the company
tested 35 CD players with
new alkaline batteries and recorded the time at which the batteries in the players "lost
power." The average time was 8.3hours with a sample standard deviation of 1.2hours.
(a)
Construct
a 95% confidence interval for the mean time until a new alkaline bat
tery used in the CD player loses power.
(b) Determine the required sample size in order to estimate the mean time until a
new alkaline battery used in the CD player losespower to within :t 10minutes
at the 99%confidence level.
EXEROSE 4.5 A sporting
equipment
company
manufactures
ISpound
dumbbells.
Toensure that the production
line is functioning properly, 50 dumbbells were selected
at random, and their weights were recorded. The observed sample mean weight of the
50 dumbbells was 16.87 lb. and the observed sample standard
deviation was 1.44lb.
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 Spring '07
 JosephGeunes
 Alex, Sample standard deviation

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