ERA CD5 Inc. wants the mean lengths of the \"cuts" on a CD to be 142 seconds {2 minutes and 22 seconds]. This will allow the disk jockeys to have plenty of time for commercials within each 10-minute segment. Assume the distribution of the length of the cuts follows a normal distribution with a standard deviation of twelve seconds. Suppose that we select a sample of 15 cuts from various CD5 sold by CRA CD5 Inc. Use appendix 3.1 for the zvalues. a. What can we say about the shape of the distribution of the sample mean? Sample mean b. What is the standard error of the mean? {Round the nal answer to 2 decimal places.) Standard error ofthe mean seconds. c. What percentage of the sarrple means will be greater than 151 seconds? [Round the nal answer to 2 decimal places.) Sample means '36 d. What percentage of the sample means will be greater than 133 seconds? (Round the nal answer to 2 decimal places.) Sample means '36 e. What percentage of the sample means will be greater than 133 but less than 151 seconds? (Round the final answer to 2 decimal places.} Sample means '36 Suppose that your statistics instructor gave six examinations during the semester. You received the following grades (percentage correct): 53, 84, 85, 71, 84, and 65. Instead of averaging the six scores, the instructor indicated he would randomly select 2 grades and report that grade to the student records office. a. How many different samples, without replacement, of 2 test grades are possible? Different samples b. Not available in Connect. c. Compute the mean of the sample means and compare it with the population mean. (Round the final answers to 2 decimal places.) The mean of the sample means is The population mean is Both means are (Click to select) v d. Would the result be different from dropping the lowest score? (Click to select) vA normal population has a mean of 83 and a standard deviation of 6. You selecta sample of 51. Use appendix 8.1 for the zvalues. Compute the probability that the sample mean is: {Round the z-values to 2 decimal places and the final answers to 4 decimal places.) 4!. Less than 82. Probability b. Between 82 and 84. Probability 1:. Between 84 and 85. Probability cl. Greater than 85. Probability