10/25/2016 1. Assignment Print View Award: 16.66 points A random sample is drawn from a population with mean = 55 and standard deviation = 4.6. Use Table 1. a. Is the sampling distribution of the sample mean with n = 13 and n = 37 normally distributed? Yes, both the sample means will have a normal distribution. No, both the sample means will not have a normal distribution. No, only the sample mean with n = 13 will have a normal distribution. No, only the sample mean with n = 37 will have a normal distribution. b. Can you use the standard normal distribution to calculate the probability that the sample mean falls between 55 and 57 for both sample sizes? Yes, for both the sample sizes, standard normal distribution could be used. No, for both the sample sizes, standard normal distribution could not be used. No, only for the sample size with n = 13, standard normal distribution could be used. No, only for the sample size with n = 37, standard normal distribution could be used. c. Calculate the probability that the sample mean falls between 55 and 57 for n = 37. (Round intermediate calculations to 4 decimal places, \"z\" value to 2 decimal places, and final answer to 4 decimal places.) Probability Hints Hint #1 References Worksheet Difficulty: 3 Hard Learning Objective: 0703 Describe the sampling distribution of the sample mean. 2. Award: 16.66 points http://ezto.mheducation.com/hm.tpx 1/5 10/25/2016 Assignment Print View A random sample of size n = 46 is taken from a population with mean = 8.7 and standard deviation = 3. Use Table 1. a. Calculate the expected value and the standard error for the sampling distribution of the sample mean. (Negative values should be indicated by a minus sign. Round "expected value" to 1 decimal place and "standard error" to 4 decimal places.) Expected value Standard error b. What is the probability that the sample mean is less than 9? (Round \"z\" value to 2 decimal places, and final answer to 4 decimal places.) Probability c. What is the probability that the sample mean falls between 9 and 8? (Do not round intermediate calculations. Round "z" value to 2 decimal places and final answer to 4 decimal places.) Probability References Worksheet Learning Objective: 0703 Describe the sampling distribution of the sample mean. Difficulty: 3 Hard Learning Objective: 0704 Explain the importance of the central limit theorem. 3. Award: 16.66 points Suppose that the milespergallon (mpg) rating of passenger cars is a normally distributed random variable with a mean and a standard deviation of 38.9 and 3.1 mpg, respectively. Use Table 1. a. What is the probability that a randomly selected passenger car gets more than 40 mpg? (Round \"z\" value to 2 decimal places, and final answer to 4 decimal places.) Probability b. What is the probability that the average mpg of three randomly selected passenger cars is more than 40 mpg? (Round \"z\" value to 2 decimal places, and final answer to 4 decimal places.) Probability c. http://ezto.mheducation.com/hm.tpx 2/5 10/25/2016 Assignment Print View If three passenger cars are randomly selected, what is the probability that all of the passenger cars get more than 40 mpg? (Round \"z\" value to 2 decimal places, and final answer to 4 decimal places.) Probability References Worksheet Difficulty: 3 Hard Learning Objective: 0704 Explain the importance of the central limit theorem. 4. Award: 16.66 points Consider a population proportion p = 0.44. a1. Calculate the expected value and the standard error of with n = 14. (Round "expected value" to 2 decimal places and "standard deviation" to 4 decimal places.) Expected value Standard error a2. Is it appropriate to use the normal distribution approximation for ? Yes No b1. Calculate the expected value and the standard error of with n = 34. (Round "expected value" to 2 decimal places and "standard deviation" to 4 decimal places.) Expected value Standard error b2. Is it appropriate to use the normal distribution approximation for ? Yes No 5. Award: 16.66 points http://ezto.mheducation.com/hm.tpx 3/5 10/25/2016 Assignment Print View A random sample of size n = 145 is taken from a population with population proportion P = 0.61. Use Table 1. a. Calculate the expected value and the standard error for the sampling distribution of the sample proportion. (Round "expected value" to 2 decimal places and "standard error" to 4 decimal places.) Expected value Standard error b. What is the probability that the sample proportion is between 0.50 and 0.70? (Round \"z\" value to 2 decimal places, and final answer to 4 decimal places.) Probability c. What is the probability that the sample proportion is less than 0.50? (Round \"z\" value to 2 decimal places, and final answer to 4 decimal places.) Probability References Worksheet Difficulty: 3 Hard Learning Objective: 0705 Describe the sampling distribution of the sample proportion. 6. Award: 16.70 points A car manufacturer is concerned about poor customer satisfaction at one of its dealerships. The management decides to evaluate the satisfaction surveys of its next 50 customers. The dealer will be fined if the number of customers who report favorably is between 29 and 41. The dealership will be dissolved if fewer than 29 customers report favorably. It is known that 71% of the dealer's customers report favorably on satisfaction surveys. Use Table 1. a. What is the probability that the dealer will be fined? (Round \"z\" value to 2 decimal places, and final answer to 4 decimal places.) Probability b. What is the probability that the dealership will be dissolved? (Round \"z\" value to 2 decimal places, and final answer to 4 decimal places.) Probability References http://ezto.mheducation.com/hm.tpx 4/5 10/25/2016 Assignment Print View Worksheet Difficulty: 3 Hard Learning Objective: 0705 Describe the sampling distribution of the sample proportion. http://ezto.mheducation.com/hm.tpx 5/5