Math 225N Week 5 Assignment_2020 {Grade A} | Math225N Week 5 Assignment_Central Limit Theorem for Proportions

Math 225N Week 5 Assignment (2020) : Central Limit Theorem for Proportions – Chamberlain College of Nursing 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=≈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=≈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.B has the larger mean. A has the larger standard deviation. 9. Question Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers. The means of A and B are equal. A has the larger standard deviation. 10. QuestionThe graph below shows the graphs of several normal distributions, labeled A, B, and C, on the same axis. Determine which normal distribution has the largest standard deviation. A 11. Question Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers. B has the larger mean.A has the larger standard deviation. 12. Question The graph below shows the graphs of several normal distributions, labeled A, B, and C, on the same axis. Determine which normal distribution has the largest mean. A Remember that the mean of a normal distribution is the x-value of its central point (the top of the "hill"). Therefore, a distribution with a larger mean will be centered farther to the right than a distribution with a smaller mean. The distribution that is farthest to the right is A, so that has the largest mean. 13. Question Which of the data sets represented by the following histograms has the smallest standard deviation?An untitled histogram has a horizontal axis labeled from 0 to 150 in increments of 50 and vertical axis labeled from 0 to 140 in increments of 20. The histogram contains vertical bars of width 6, starting at the horizontal axis value of 75. The approximate heights of the bars as follows, where the horizontal axis label is listed first and the approximate height is listed second: 75, 6; 82, 18; 88, 70; 76, 115; 82, 150; 88, 103; 95, 70; 102, 20; 108, 8. Remember that the standard deviation is a measure of how spread out the data is. If the values are concentrated around the mean, then a data set has a lower standard deviation. A histogram with a taller hill indicates higher frequencies of the same values, and has a lower standard deviation than a histogram with a shorter hill and a wider range of values.- - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - 33. Question Of the 13,500 savings accounts in a bank, 4,675 belong to people younger than 40 years old. The bank president would like to increase her institution's marketing strategy to younger customers, so she is examining the population proportions in order to create a statistical study. Find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of size n=400. The population proportion is p=4,675/13,500≈0.346. This is also the mean of the sampling distribution: μp^=p=0.346 For samples of size n=400, the standard deviation of the sampling distribution is σpˆ=p(1−p)n−−−−−−−√=0.346(1−0.346)400−−−−−−−−−−−−−−√≈0.024 34. A baseball team calls itself "America's Favorite Team," because it has 90,000 fans on social media out of 2,210,000 social media users. Find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of size n=1,000. Round all answers to 3 decimal places. The population proportion is p=90,000/2,210,000≈0.041. This is also the mean of the sampling distribution:μp^=p=0.041 For samples of size n=1,000, the standard deviation of the sampling distribution is σpˆ=p(1−p)n−−−−−−−√=0.041(1−0.041)1,000−−−−−−−−−−−−−−√≈0.006 35. Question A study by doctors of children attending a certain elementary school finds that, of 812 students, 245 watch more than 2 hours of television each day. Find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of size n=100 students. Round all answers to 3 decimal places. The population proportion is p=≈0.302 . This is also the mean of the sampling distribution: μp^=p=0.302 For samples of size n=100 , the standard deviation of the sampling distribution is σpˆ=p(1−p)n−−−−−−−√=0.302(1−0.302)100−−−−−−−−−−−−−−√≈0.046 36. Pharmacy technicians are concerned about the rising number of fraudulent prescriptions they are seeing. A small pharmacy sees 1,500 new prescriptions a month, 28 of which are fraudulent. Find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of size n=180. Round all answers to 3 decimal places. The population proportion is p=281,500≈0.019. This is also the mean of the sampling distribution:μp^=p=0.019 For samples of size n=180, the standard deviation of the sampling distribution is σpˆ=p(1−p)n−−−−−−−√=0.019(1−0.019)180−−−−−−−−−−−−−−√≈0.010 37. 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. The population proportion is p=≈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 38. 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