5. Suppose that it takes a nurse on average 13.7 minutes to complete a specic task and that completion time is normally distributed with a standard deviation of 3.4 minutes. a. What proportion of nurses complete the task between 15.2 and 17.7 minutes? b. What proportion of nurses complete the task in less than 8 minutes and 24 seconds? c. What completion time is the 73rd percentile? d. If 30 nurses were randomly selected from this population, what is the probability that the sample mean time will be greater than 14 minutes and 12 seconds? 6. Assume the same population of nurses above with the same parameters and that they are from Chimney Rock Hospital. Additionally, assume a second population of nurses from Topsail Hospital clocks a mean completion time of 12.6 minutes with a standard deviation of 4.2 minutes and completion time is normally distributed. Suppose 15 and 10 nurses were randomly selected from Chimney Rock and Topsail Hospitals, respectively, and that these samples produced sample means of 12.8 and 13.3 minutes, respectively. What is the probability of observing a difference in sample means of less than the absolute value of the difference in observed sample means, i.e., the difference in observed sample means without regard to hospital order