1. The following is the data on the diameter of a bolt meant for a sensitive machine. To make it simple for you we will use a finite dataset. The values are in millimeters.

sample #	obs 1	obs 2	obs 3	obs 4	obs 5
1	2.1	1.9	1.8	2.2	1.80
2	1.98	1.95	1.87	2.05	2.1
3	2.1	2.0	1.95	2.02	2.2
4	3.0	2.5	2.2	1.98	2.15

What is the UCL of the chart. Nothing else is given. Round your answer to THREE places of decimal, and do not round intermediate values.

2. You are to construct an appropriate statistical process control chart for the average time (in seconds) taken in the execution of a set of computerized protocols. Data was collected for 30 samples each of size 40, and the mean of all sample means was found to be 37. What is the LCL of a 2.70 control chart? The standard deviation of the sample-means was known to be 4.5 seconds. Your answer should be rounded to ONE place of decimal.

3. You are to construct a 3.02-sigma statistical process control chart to monitor the proportion of customers who rate the service provided by a medical center to be "below average". The data is taken from samples of size 250. You will enter the UCL of the chart only. Round your answer to THREE places of decimal.

Sample #	customers
1	20
2	30
3	25
4	15
5	22
6	28
7	30
8	40
9	20
10	40