This box plot graphic below shows the comparison of eight group of people for computer vision test score.

1. Which group has the lowest score?
2. Which group has the highest score?
3. Which group has the highest median?
4. Which group has the lowest 25^th percentile?
5. Which group has the highest 75^th percentile?

Question 2

The life of an automotive battery is normally distributed with mean 900 days and standard deviation 35 days. What fraction of these batteries would be expected to survive beyond 1,000 days?

Question 3

The time to failure in hours of an electronic component subjected to an accelerated life test is shown in the following table. To accelerate the failure test, the units were tested at an elevated temperature (read down, then across).

Electronic Component Failure Time
127	124	121	118
125	123	136	131
131	120	140	125
124	119	137	133
129	128	125	141
121	133	124	125
142	137	128	140
151	124	129	131
160	142	130	129
125	123	122	126

(a) Calculate the sample average and standard deviation.

(b) Construct a histogram.

(c) Construct a stem-and-leaf plot.

(d) Find the sample median and the lower and upper quartiles.

Question 4

(a) Consider the following data taken on subgroups of size 5. The data contains 20 averages and ranges on the diameter (in millimeters) of an important component part of an engine. Display Xbar and R-charts. Does the process appear to be in control? (Do not use 3 sigma to construct the charts. Instead use the Factors For Control Charts provided in Lectures 3 and 4).

Sample	Xbar	R
1	2.3972	0.0052
2	2.4191	0.0117
3	2.4215	0.0062
4	2.3917	0.0089
5	2.4151	0.0095
6	2.4027	0.0101
7	2.3921	0.0091
8	2.4171	0.0059
9	2.3951	0.0068
10	2.4215	0.0048
11	2.3887	0.0082
12	2.4107	0.0032
13	2.4009	0.0077
14	2.3992	0.0107
15	2.3889	0.0025
16	2.4107	0.0138
17	2.4109	0.0037
18	2.3944	0.0052
19	2.3951	0.0038
20	2.4015	0.0017

(b) Suppose that the buyer has set specifications for the part. The specifications require that the diameter fall in the range covered by 2.40000 ± 0.0100 mm. What proportion of units produced by this process will not conform to specifications?

Question 5

Briefly discuss the relationship between Average Run Length (ARL) and Type I (a – alpha) and Type II (b– Beta) errors relative to the control chart. What practical implication in terms of process operation do these two types of errors have? (Requires research, please cite all your work).

100- 90- 80- 70- 60- 50 40- 30 20- 10- 0 Computer Vision Test Scores Group A Group B Group C Group D Group E Group F Group G Group H