In order to estimate the mean 30-year fixed mortgage rate for a home loan in the United States, a random sample of 15 recent loans is taken. The average calculated from this sample is 7.85%. It can be assumed that 30-year fixed mortgage rates are normally distributed with a standard deviation of 0.6%. Compute 90% and 95% confidence intervals for the population mean 30-year fixed mortgage rate. Use Table 1. (Round intermediate calculations to 4 decimal places. Round "z-value" to 3 decimal places and final answers to 2 decimal places. Enter your answers as percentages, not decimals.) Confidence Level Confidence Interval
90% % to %
95% % to %

Imagine us is a startup that offers high definition 3d prenatal ultrasounds for high-end customers. the service process includes four activities that are conducted in the sequence described below. (the time required for each activity is shown in parentheses): activity 1: welcome a patient and explain the procedure. (20 minutes)activity 2: prep the patient (e.g., show them to the room, apply ultrasound gel). (17 minutes) (*your id number represents the amount of time needed to complete this task)activity 3: take images. (5 minutes)activity 4: discuss diagnostic with patient. (20 minutes)at each location there are employees (servers) s1, s2, and s3. the assignment of tasks to servers is the following: s1 does activities 1 and 2.s2 does activity 3.s3 does activity 4.a. what is the capacity of this process (in customers per hour)? b. suppose 3 patients arrive every hour on average. ignoring any “start of day” or “end of day” effects, what are the utilizations of all three servers (%)? c. suppose each activity can be done by any server and any server can do any set of activities. however, each activity is done by only one server. for example, a possible assignment includes: s1 does activity 1, s2 does activity 2, and s3 does activities 3 and 4. of course, the original assignment of servers to activities is also feasible. what is the maximum capacity of the process (in customers per hour)? d. now consider the capacity measures in (c) and (a), what is the percentage change? why can you improve capacity without using additional resources? (there is no free lunch, right? )note: for all hw assignments, show your process of getting the results. only providing the final answers is not acceptable and will get 0%. if necessary, use a separate sheet of paper to show your work.