MATH 225N Week 5 Assignment: Central Limit Theorem for Proportions

MATH 225N Week 5 Assignment:
Central Limit Theorem for
Proportions

, MATH 225N Week 5 Assignment: Central Limit Theorem for
Proportions
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:

μpp^=p=0.600

For samples of size n=60, the standard deviation of the sampling distribution is

σppˆ=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

σppˆ=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

, σppˆ=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
σppˆ=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:

μpp^=p=0.256

For samples of size n=40, the standard deviation of the sampling distribution is

σppˆ=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:

μpp^=p=0.106

For samples of size n=121, the standard deviation of the sampling distribution is

σppˆ=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