Central Limit Theorem for Proportions
Week 5 Assignment:
1. A 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
of the sampling distribution for samples of size n=60.
Correct answers:
10 point 6 0 0 $0.600$0.600
20 point 6 0 0 $0.600$0.600
30 point 0 6 3 $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
, σpˆ=p(1−p)n−−−−−−−√=0.256(1−0.256)40−−−−−−−−−
−−−−−√≈0.069
6. A marketing team is targeting people who might buy a hybrid car. In their
city, with a population of 30,000 people, 3,170 people either drive a
hybrid car or have indicated on a recent survey that they would be interested
in driving one. Find the population proportion, as well as the mean and standard
deviation of the sampling distribution for samples of size n=121.
he population proportion is p=3,17030,000≈0.106. This is also the
mean of the sampling distribution:
μp^=p=0.106
For samples of size n=121, the standard deviation of the sampling
distribution is
σpˆ=p(1−p)n−−−−−−−√=0.106(1−0.106)121−−−−−−−−−
−−−−−√≈0.028
7. A brokerage company is analyzing its retirement accounts for its clients nearing
retirement. From recent survey data, the proportion of adults in the United States who say
they are financially ready for retirement is 31%. For a random sample of size 85, what is
standard deviation for the sampling distribution of the sample proportions, rounded to
three decimal places?
Given the population proportion p=31%=0.31 and a sample size of n=85,
the standard deviation of the sampling distribution of sample proportions is
σpˆ=p(1−p)n−−−−−−−√=0.31(1−0.31)85−−−−−−−−−−−
−√≈0.050
8. Question
Given the plot of normal distributions A and B below, which of the following
statements is true? Select all correct answers.
Week 5 Assignment:
1. A 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
of the sampling distribution for samples of size n=60.
Correct answers:
10 point 6 0 0 $0.600$0.600
20 point 6 0 0 $0.600$0.600
30 point 0 6 3 $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
, σpˆ=p(1−p)n−−−−−−−√=0.256(1−0.256)40−−−−−−−−−
−−−−−√≈0.069
6. A marketing team is targeting people who might buy a hybrid car. In their
city, with a population of 30,000 people, 3,170 people either drive a
hybrid car or have indicated on a recent survey that they would be interested
in driving one. Find the population proportion, as well as the mean and standard
deviation of the sampling distribution for samples of size n=121.
he population proportion is p=3,17030,000≈0.106. This is also the
mean of the sampling distribution:
μp^=p=0.106
For samples of size n=121, the standard deviation of the sampling
distribution is
σpˆ=p(1−p)n−−−−−−−√=0.106(1−0.106)121−−−−−−−−−
−−−−−√≈0.028
7. A brokerage company is analyzing its retirement accounts for its clients nearing
retirement. From recent survey data, the proportion of adults in the United States who say
they are financially ready for retirement is 31%. For a random sample of size 85, what is
standard deviation for the sampling distribution of the sample proportions, rounded to
three decimal places?
Given the population proportion p=31%=0.31 and a sample size of n=85,
the standard deviation of the sampling distribution of sample proportions is
σpˆ=p(1−p)n−−−−−−−√=0.31(1−0.31)85−−−−−−−−−−−
−√≈0.050
8. Question
Given the plot of normal distributions A and B below, which of the following
statements is true? Select all correct answers.
