Question

You have just started at a company and they present you with historical data for the time in minutes that it takes to prepare a solar panel. The company has 3 locations and they give you the following sample data:

Minutes to Prepare A Solar Panel
Site 1	Site 2	Site 3
119.5	120.3	128.1
118.0	100.0	126.6
114.4	107.2	123.5
118.6	118.4	125.5
126.9	111.6	127.3
122.0	113.1	118.3
116.1	102.9	125.6
136.5	103.2	128.2
119.5	100.3	126.1
124.7	99.3	120.6
121.7	89.3	123.3
110.2	100.9	137.4
119.0	116.7	122.7
123.7	112.8	127.0
120.5	101.8	123.3
122.5	106.8	122.9
124.9	107.7	114.3
121.9	111.8	121.3
120.7	103.5	127.1
122.4	111.8	127.6
118.6	103.6	127.7
120.5	104.8	130.6
111.6	126.0	119.3
120.6	114.5	122.2
116.2	106.3	123.8
123.5	105.4	121.7
126.4	108.6	113.6
118.5	114.7	123.5
116.0	130.4	131.9
122.1	104.5	123.6
123.5	108.3	130.4
115.6	105.6	127.0
124.8	114.2	123.1
119.3	98.3	115.9
113.1	100.0	121.9
116.8	117.9	123.9
123.0	116.4	121.7
115.8	113.2	131.6
119.3	118.0	124.8
119.2	108.1	123.9

They are interested in characterizing the data at these three locations. The QC manager stated that their goal is 120 min or less because then they could (ideally) make 4 per 8 hour day.

1. Determine if the data are normally distributed and list the mean and standard deviation for each site. Please include all necessary graphs.
2. Using both histograms and box plots, explain how the graphical data supports the approach to the characterization of the data described in question a

Answer 1

Based on the above-created box plot and histogram it seems that Site 1 and Site 2 are Right and positively skewed because data from these two sites are low at higher ends and in the beginning, it reaches its top. The tail of these two sites seems towards the right side of the graph.

Site 3 data, seems to be normally distributed as both sides' data distribution is approximately equal or symmetric.

To know whether the data follows normal distribution or not one should look for the symmetric ness of the distribution of the data. Which means both sides of the central tendency data distribution is approximately symmetrical.