the goal of this assignment is to complete all the exercises provided in the word document.
Quiz 8.2 1. Assume that there is a mayoral election coming up in a certain city and 44% of the voters in the city support a certain candidate. A sample of 380 voters is polled, and the proportion p^ of voters who support the candidate is calculated. Find the probability that proportion of voters in the sample who support the candidate is within 3% of the assumed population proportion of 44%. Round your answer to 4 decimal places. 2. Approximately 15% of the population is left-handed. Assume that a sample of 151 people is selected and the sample proportion p^ of left-handed individuals is calculated. Find the probability that proportion of people in the sample who are left handed is within 4% of the true population proportion. Round your answer to 4 decimal places. 3. Approximately 70% of high school students in the United State graduate within 4 years. Suppose a random sample of 75 high school students who were scheduled to graduate last year is obtained, and the proportion p^ of students who graduated within 4 years is calculated. Find the probability that p^ is greater than 0.73. Round your answer to 4 decimal places. 4. Approximately 37% of people in the United State have a blood type of O+. Assume that a sample of size 133 is drawn and the proportion p^ of individuals in the sample with type O+ blood is calculated. Find the probability that sample proportion is within 0.03 of the true population proportion. Round your answer to 4 decimal places. 5. A mortgage company classifies its borrowers into three categories: Low Risk, Medium Risk, and High Risk. From experience, the company knows that: · 2% of low risk borrowers eventually default on their mortgages. · 9% of medium risk borrowers eventually default on their mortgages. · 14% of high risk borrowers eventually default on their mortgages. The mortgages for 135 high risk borrowers are put together into one portfolio. The company determines that they will profit on the portfolio as long as no more than 19% of borrowers with mortgages in the portfolio default. What is the probability that the company makes a profit on the portfolio? Round your answer to 4 decimal places. Quiz 8.1 1. The mean salary of people living in a certain city is $37500 with a standard deviation of $1589. A sample of 46 people is selected at random from those living in the city. Find the probability that the mean income of the sample is less than $38000. Round your answer to 4 decimal places. 2. The mean salary of people living in a certain city is $37500 with a standard deviation of $2191. A sample of 49 people is selected at random from those living in the city. Find the probability that the mean income of the sample is within $500 of the population mean. Round your answer to 4 decimal places. 3. IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. A sample of 6 people is selected at random. Find the probability that the mean IQ of people in the sample is greater than 105. Round your answer to 4 decimal places. 4. IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. A sample of 20 people is selected at random. Find the probability that the mean IQ of people in the sample is within 8 points of the population mean IQ. Round your answer to 4 decimal places. 5. The duration of human pregnancies is approximately normally distributed with a mean of 272 days and a standard deviation of 9 days. A sample of 5 pregnancies is selected at random. Find the probability that the mean duration of the sample is less than 266. Round your answer to 4 decimal places. 6. The duration of human pregnancies is approximately normally distributed with a mean of 272 days and a standard deviation of 9 days. A sample of 5 pregnancies is selected at random. Find the probability that the mean duration of the sample is within 4 days of the population mean duration. Round your answer to 4 decimal places. 7. Assume that the height of adult females in the United States is approximately normally distributed with a mean of 63.9 inches and a standard deviation of 2.82 inches. A sample of 10 such women is selected at random. Find the probability that the mean height of the sample is greater than 62.7 inches. Round your answer to 4 decimal places. 8. Assume that the height of adult females in the United States is approximately normally distributed with a mean of 64 inches and a standard deviation of 2.75 inches. A sample of 5 such women is selected at random. Find the probability that the mean height of the sample is within 1.4 inches of the population mean height. Round your answer to 4 decimal places. 9. The mean salary of people living in a certain city is $37500 with a standard deviation of $2330. A sample of n people will be selected at random from those living in the city. Find the smallest sample size n that will guarantee at least a 90% chance of the sample mean income being within $500 of the population mean income. Round your answer up to the next largest whole number. 10. IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. A sample of n people will be selected at random. Find the smallest sample size n that would guarantee at least a 95% chance that the mean IQ of the sample is within 15 points of the population mean. Round your answer up to the next largest whole number. Quiz 9.0 1. The following confidence interval is constructed for a population mean, μ: (14.7, 23.1) Find the sample mean x¯ used to construct the confidence interval. 2. The following confidence interval is constructed for a population mean, μ: (105.9, 117.9) Find ε, the margin of error for the confidence interval. 3. The following confidence interval is constructed for a population mean, μ: (33.9, X) The sample mean used to construct the confidence interval was x̄ = 44. Find X. 4. The following confidence interval is constructed for a population proportion, p: (0.327, 0.453) Find the sample proportion p^ used to construct the confidence interval. 5. A researcher conducts a poll to study the level of educational attainment in a certain state. Of those polled, 18.5% had a college degree. In order to estimate the proportion of the overall population in the state who had college degrees, the researcher created a 90% confidence interval, a 95% confidence interval, and a 99% confidence interval for p. Those intervals are provided below, in no specific order. Interval 1: (0.1340, 0.2360) Interval 2: (0.1179, 0.2521) Interval 3: (0.1421, 0.2279) Quiz 9.1 1. A media analyst is trying to determine the proportion of people living in St. Louis that watch a particular television show. The analyst collects a random sample of 161 people from St. Louis. Of the 161 people in the sample, 42 people said that they did watch the show. a) Find a 95% confidence interval for the true population proportion of people in St. Louis who watch the show. b) Provide the right endpoint of the interval as your answer. Round your answer to 4 decimal places. 2. A media analyst is trying to determine the proportion of people living in St. Louis that watch a particular television show. The analyst collects a random sample of 182 people from St. Louis. Of the 182 people in the sample, 38 people said that they did watch the show. a) Find a 95% confidence interval for the true population proportion of people in St. Louis who watch the show. b) Provide the margin of error of the interval as your answer. Round your answer to 4 decimal places. 3. A medical researcher is interested in knowing what percentage of the U.S. population has a certain gene. The researcher collect a random sample of 520 people from across the country, and tests them for the gene. The gene was present in 40 of the 520 people tested. a) Find a 90% confidence interval for the true proportion of people in the U.S. with the gene. b) Provide the right endpoint of the interval as your answer. Round your answer to 4 decimal places. 4. A medical researcher is interested in knowing what percentage of the U.S. population has a certain gene. The researcher collect a random sample of 514 people from across the country, and tests them for the gene. The gene was present in 52 of the 514 people tested. a) Find a 90% confidence interval for the true proportion of people in the U.S. with the gene. b) Provide the margin of error of the interval as your answer. Round your answer to 4 decimal places. 5. A newspaper polls 51 voters to ask which candidate for mayor the supported in an upcoming election. Of the 51 people polled, 25 said that they intended to vote for Candidate Jones. a) Find a 99% confidence interval for the true proportion of people in the city who plan to vote for Candidate Jones. b) Provide the right endpoint of the interval as your answer. Round your answer to 4 decimal places. 6. A newspaper polls 71 voters to ask which candidate for mayor the supported in an upcoming election. Of the 71 people polled, 31 said that they intended to vote for Candidate Jones. a) Find a 99% confidence interval for the true proportion of people in the city who plan to vote for Candidate Jones. b) Provide the margin of error of the interval as your answer. Round your answer to 4 decimal places. 7. A researcher conducts a poll to study the level of educational attainment in a certain state. Of the 174 people surveyed by the researchers, 43 had a bachelor's Degree. a) Find a 90% confidence interval for the true proportion of people the state with bachelor's degrees. b) Provide the right endpoint of the interval as your answer. Round your answer to 4 decimal places. 8. A researcher conducts a poll to study the level of educational attainment in a certain state. Of the 281 people surveyed by the researchers