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Session Review
Statistics 226
Supplemental Instruction
Iowa State University
Leader:
Course:
Instructor:
Date:
Luyun
Stat 226
Anna Peterson
2/23/16
Sampling distribution:
The sampling distribution of a statistic (e.g. the sample mean ) is the distribution of
__________ taken by the statistic in ______________________ from the same population.
For every sampling distribution we can specify the:
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Sampling distribution
when population is normal
Assume X~ N (μ, σ2). The distribution of the sample mean
is
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Exercise:
1. A bottling company uses a machine to fill bottles with Cola. The bottles are supposed to
contain 300 ml. in fact, the contents vary according to a normal distribution with mean μ
= 298 ml and standard deviation σ = 3 ml.
What proportion of individual bottles contains less than 295 ml?
What proportion of 6 packs have a sample mean contents that is less than 295 ml?
2. According to Chance magazine the mean healthy body temperature is around μ = 98.6 °F
with a variance of σ2 = 0.36 °F. The distribution of the body temperature is known to
follow normal distribution.
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What proportion of humans has a temperature at or above the presumed population mean
of 98.6 °F?
Suppose we take a random samples of 16 adults. What proportion of samples of size 16
have a sample mean temperature at or above the presumed population mean of 98.6 °F?
Suppose we take a random samples of 16 adults. What proportion of samples of size 16
have a sample mean temperature at or below 98.5 °F?
3. The scores of the students on the ACT college entrance examination in a recent year had
a Normal distribution. With mean equals to 18.6 and a standard deviation of 5.9.
a. What is the probability that a single student randomly chosen from all those taking the
test scores or higher?
b. Now take a simple random sample of 50 students who took the test. What are the mean
and standard deviation of the sample mean score x of these students?
c. What is the probability that the mean score of these students is 21 or higher?