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MATH 225N Week 5 Assignment: Central Limit Theorem for Proportions-PASS
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MATH 225N Week 5 Assignment: Central Limit Theorem for Proportions
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CentraLl i roportionmiTt s
heoremfoP
r
Week5Assi
gnment:
of the sam 1A dental student is conducting a study on the number of people
who visit
their dentist regularly. Of the 520 people surveyed, 312 indicated that they
had visited their dentist within the past year.
Find the population proportion, as well as the mean and standard
deviation pling distribution for samples of size n=60.
Correct answers:
10 point 6 0 0 $0.600$0.600
0 point 6 0 02
$0.600$ 0.600
0 point 0 6 33 $0.063$
0.063
The population proportion is p=312520≈0.600. This is also the mean of
the sampling distribution:
μp^=p=0.600
For samples of size n=60, the standard deviation of the sampling
distribution is
σpˆ=p(1−p)n−−−−−−−√=0.600(1−0.600)60−−−−−−−−−
−−−−−√≈0.063
2. From recent census data, it is discovered that the proportion of the adults
in the United States who are first generation Americans is 14%. For a
random sample of size 500, what is standard deviation for the sampling
distribution of the sample proportions, rounded to three decimal places?
---Given the population proportion p=14%=0.14 and a sample size of
,n=500, the standard deviation of the sampling distribution of sample
proportions is
σpˆ=p(1−p)n−−−−−−−√=0.14(1−0.14)500−−−−−−−−−−
−−√≈0.016
, 3. From recent survey data, a car buying business finds that 12.5% of the
proportion of adults in a city would be likely to use their services. For a random
sample of 115 people, what is standard deviation for the sampling distribution
of the sample proportions,
rounded to three decimal
places?
Given the population proportion p=12.5%=0.125 and a sample
size of n=115, the standard deviation of the sampling distribution
of sample proportions is
σpˆ=p(1−p)n−−−−−−−√=0.125(1−0.125)115−−−−−−−−−
−−−−−√≈0.031
4. Question
From recent survey data, its known that the proportion of adults in the United
States who are smokers is 18%. For a random sample of size 150, what is
standard deviation for the sampling distribution of the sample proportions,
rounded to three decimal places?
Given the population proportion p=18%=0.18 and a sample size of
n=150, the standard deviation of the sampling distribution of sample
proportions is σpˆ=p(1−p)n−−−−−−−√=0.18(1−0.18)150−−−
−−−−−−−
−−√≈0.031
5.A small community college has a population of 986 students, 252 of
whom them are considered non-traditional students.
Find the population proportion, as well as the mean and standard
deviation of the sampling distribution for samples of size n=40.
Round all answers to 3 decimal places.
The population proportion is p=252986≈0.256. This is also the mean of
the sampling distribution:
μp^=p=0.256
For samples of size n=40, the standard deviation of the sampling
distribution is
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