Question 2 ( 10 marks) a. Suppose a population has mean p = 85 and standard deviation o = 20. Suppose a random sample of size n = 35 is selected. i. What is the mean of the distribution of sample means? [1] ii. What is the standard deviation of the distribution of sample means (standard error)? [1] b. Suppose the mean length of time that a caller is placed on hold when calling a customer service center is 40. 1 seconds, with a standard deviation of 10.2 seconds. Find the probability that the mean length of time on hold in a sampleof 30 calls will be at least 35 seconds? [3] WSTC 2022.3 STATISTICAL DECISION MAKING INTRA-TERM EXAM 2 Page 4 of 14 Question 2 ( cont.) Marks c. The percentage of Australian households that have online connections is 76.5%. Suppose a government department is conducting a follow-up study and randomly selects a sample of 150 households, what is the probability that more than 120 of these households have online connections? [3] d. If a random sample of 200 is taken, how does this change your answer in part (c). [2]