MATH 225N Week 5 Assignment; Central Limit Theorem for Means

1. Question: A family of statisticians is trying to decide if they can afford for their child to play youth baseball. The cost of joining a team is normally distributed with a mean of $750and a standard deviation of $185. If a sample of 40teams is selected at random from the population, select the expected mean and standard deviation of the sampling distribution below. 2. Question: A cupcake baker is planning a supplies order and needs to know how much flour he needs. He knows that his recipes use an average of 100grams of flour, normally distributed, with a population standard deviation of 15grams. If he is consulting a sample size of 30recipes, select the mean and standard deviation of the sampling distribution to help him order his supplies from the options below. 3. Question: A head librarian for a large city is looking at the overdue fees per user system-wide to determine if the library should extend its lending period. The average library user has $19.67in fees, with a standard deviation of $7.02. The data is normally distributed and a sample of 72library users is selected at random from the population. Select the expected mean and standard deviation of the sampling distribution from the options below. 4. Question: A well known social media company is looking to expand their online presence by creating another platform. They know that they current average 2,500,000users each day, with a standard deviation of 625,000users. If they randomly sample 50days to analyze the use of their existing technology, identify each of the following, rounding to the nearest whole number if necessary: 5. Question: A bank is reviewing its risk management policies with regards to mortgages. To minimize the risk of lending, the bank wants to compare the typical mortgage owed by their clients against other homebuyers. The average mortgage owed by Americans is $306,500, with a standard deviation of $24,500. Suppose a random sample of 150Americans is selected. 6. Question: The average time it takes a certain brand of ibuprofen to start working is 25minutes, with a standard deviation of 13minutes, distributed normally. A pharmacist randomly samples 20pills from this brand, because she is researching different brands in order to find the quickest acting ibuprofen to recommend to her customers. Identify the following to help her make her recommendations, rounding to the nearest hundredth if necessary: 7. Question: Major league baseball recruiters are analyzing college players as potential draft choices. In a survey of college baseball players, the recruiters found that they hit an average of 13home runs per season, with a standard deviation of 5. Suppose a random sample of 45baseball players is selected. Identify each of the following and remember to round to the nearest whole number: 8. Question: The average credit card debt owed by Americans is $6375, with a standard deviation of $1200. Suppose a random sample of 36Americans is selected. Identify each of the following: 9. Question: The heights of all basketball players are normally distributed with a mean of 72inches and a population standard deviation of 1.5inches. If a sample of 15players are selected at random from the population, select the expected mean of the sampling distribution and the standard deviation of the sampling distribution below. 10. Question: The owners of a baseball team are building a new baseball field for their team and must determine the number of seats to include. The average game is attended by 6,500fans, with a standard deviation of 450people. Suppose a random sample of 10games is selected to help the owners decide the number of seats to include. Identify each of the following and be sure to round to the nearest whole number: 11. Question: The Washington Wheat Farmers Club is studying the impact of rising grain prices on their members' planting habits. The club members produce an average of 150million bushels of wheat per year, with a standard deviation of 18million bushels. The club takes a random sample of 35years to create a statistical study. Identify each of the following, rounding to the nearest hundredth when necessary: 12. Question: Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers…… A curve labeled A rises to a maximum near the left of the horizontal axis and the falls. Another curve labeled B rises to a maximum to the right of and below curve A and falls. 13. 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 standard deviation….. A figure consists of three curves along a horizontal axis, labeled Upper A, Upper B and Upper C. Curve Upper A is farthest to the right, curve Upper B is tall and skinny, and curve Upper C is farthest to the left. 14. Question: Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers……A figure consists of two curves labeled Upper A and Upper B. The curve Upper A is tall and evenly spread out from the center and the curve Upper is B is shorter and more spread out than A. 15. Question: Which of the following lists of data has the smallest standard deviation? 16. Question: Which of the following lists of data has the smallest standard deviation? 17. Question: Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers…… A figure consists of two curves labeled Upper A and Upper B. Curve Upper A is shorter and more spread out than curve Upper B, and the curve Upper B is taller and farther to the right than curve Upper A….. 18. 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 smallest standard deviation….. A figure consists of three curves along a horizontal axis, labeled Upper A, Upper B and Upper C. Curve Upper A is evenly spread out, curve Upper B is tall and the least spread out, and curve Upper C is short and more evenly spread out from the center. 19. 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 smallest standard deviation…...A figure consists of three curves along a horizontal axis, labeled Upper A, Upper B and Upper C. Curve Upper A is farthest to the left from the center, curve Upper B is evenly spread out to the right from the center, and curve Upper C is tall and the least spread out. 20. 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 smallest mean…..A curve labeled B rises to a maximum and then falls. A curve labeled A rises to a maximum below and to the right of A and then falls. A curve labeled C rises to a maximum to the right of and below the maximum of A. 21. 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 smallest mean…. A figure consists of three curves along a horizontal axis, labeled Upper A, Upper B and Upper C. Curve Upper A is farthest to the left, curve Upper B is farthest to the right, and curve Upper C is tall and skinny…. 22. Question: A head football coach is concerned about the weight gain of some of his players. He finds that the weight of all football players is normally distributed with a mean of 250 pounds and a population standard deviation of 54 pounds. If the coach selects a random sample of 10 players from the population, identify the expected mean and the standard deviation of the sampling distribution below. 23. Question: A businesswoman wants to open a coffee stand across the street from a competing coffee company. She notices that the competing company has an average of 170customers each day, with a standard deviation of 45customers. Suppose she takes a random sample of 31days. Identify the following to help her decide whether to open her coffee stand, rounding to the nearest whole number when necessary: