Please help answering the questions below with an extensive explanation.

#1) Following are five types of problems that can occur while answering customer calls by the customer service representatives of Infinite Streaming TV.

--- customer spends too much time on "hold

--- customer representative gives wrong information

--- customer representative is unprofessional

--- customer is transferred to the wrong department

--- customer is disconnected

Last month, a total of 468 calls were subject to a quality audit. Results obtained are summarized below:

Number of problems per call Frequency

1. 73
2. 10
3. 5
4. 1
5. 0

Compute DPMO for the above data.

#2) ABC drug store operates a walk-in COVID vaccination clinic at their facility. Correct vaccination procedure involves giving the correct dosage and the correct vaccination (e.g. Pfizer, Moderna etc.) to each patient. Over the last quarter, 1200 shots were administered at the clinic. In the last quarter, they found that two patients received incorrect vaccination, two other patients received incorrect dosage and 4 other patients received incorrect vaccination and incorrect dosages.

Compute DPMO of the process.

#3) Specification limits for the width of a part produced in a new machine is 3 0.008 centimeters. The standard deviation of the process is estimated to be 0.003 centimeters.

What percentage of the parts would be outside the specifications for the width of the part, if the process was operated while centered at 3.000 centimeters? Assume normal distribution of measurements.

#4) As a Purchasing Manager, you need to make some decisions regarding the procurement of bolts from the following suppliers. The diameter at the end of the bolt has specifications of 1.500 0.009 inches. Each of the two suppliers have reported the sample mean and sample standard deviation of their bolt diameters computed from random samples of their production runs.The suppliers' process statistics are shown below:

Supplier	Sample Mean (inches)	Sample Standard Deviation (inches)
A	1.500	0.0022
B	1.495	0.0015

Using process capability criteria, determine which supplier would you recommend? Provide justification for your recommendation?

#5) Pizza store sells 1-size circular pizzas. Based on customer survey, the store expects their customers to be satisfied with pizza crust between 28-32 centimeters in diameter. Sample data collected indicate that the pizza crust averages 30 centimeters in diameter, with a standard deviation of 1.1 centimeters.

Is the pizza store capable (use process capability calculations) of meeting its customer requirements? If not, what options does the store have to rectify the situation?