# Descripitve Stats Paper

**Topics:**Randomness, Standard deviation, Normal distribution

**Pages:**17 (3106 words)

**Published:**May 23, 2013

Question 1: The data shown below are chemical process yield on successive days. Construct a histogram for these data. 94.1| 87.3| 94.1| 92.4| 84.6| 85.4|

93.2| 84.1| 92.1| 90.6| 83.6| 86.6|

90.6| 90.1| 96.4| 89.1| 85.4| 91.7|

91.4| 95.2| 88.2| 88.8| 89.7| 87.5|

88.2| 86.1| 86.4| 86.4| 87.6| 84.2|

86.1| 94.3| 85.0| 85.1| 85.1| 85.1|

95.1| 93.2| 84.9| 84.0| 89.6| 90.5|

90.0| 86.7| 87.3| 93.7| 90.0| 95.6|

92.4| 83.0| 89.6| 87.7| 90.1| 88.3|

87.3| 95.3| 90.3| 90.6| 94.3| 84.1|

Question 2: The time to failure in hours of an electronic component subjected to an accelerated life test is given below. Construct histogram of these data 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| 132|

160| 142| 130| 129|

125| 123| 122| 126|

Question 3: The tensile strength of a metal part is normally distributed with mean 40 lb and standard deviation 8 lb. If the lower specification limit is 34 lb and upper specification limit is 48 lb, Find out the % of parts fail to meet specification?

Question 4: The output voltage of a power supply is normally distributed with mean 12 V and standard deviation 0.05 V. If the specification are at 12 0.1 V, calculate the total % rejection?

Question 5: The life of an automotive battery is normally distributed with mean 900 days and standard deviation 35 days. What % of these batteries would be expected to survive beyond 1000 days?

Question 6: The following data shows the diameter (in inches) of a sample of 40 ball bearings manufactured by certain process 0.738| 0.729| 0.743| 0.740|

0.735| 0.731| 0.726| 0.737|

0.728| 0.737| 0.724| 0.735|

0.745| 0.736| 0.728| 0.742|

0.733| 0.742| 0.739| 0.725|

0.735| 0.732| 0.734| 0.738|

0.732| 0.735| 0.735| 0.736|

0.737| 0.731| 0.733| 0.729|

0.736| 0.735| 0.738| 0.736|

0.730| 0.740| 0.734| 0.733|

If the specification is 0.734 0.02, Calculate the process capability index Cp & Cpk?

Question 7: The data shown below are the deviations from the nominal diameter for holes drilled in a carbon-fibre composite material used in aerospace manufacturing. The values reported are deviations in ten thousands of an inch. -30| 50| -20| 10| 30|

0| 50| -60| -20| 30|

-50| 10| 20| 30| 20|

-10| -10| 30| -20| 50|

20| -40| 50| 20| 10|

0| 0| 40| -40| 20|

0| 0| 20| -20| -10|

70| -30| 30| -10| 0|

0| 0| 20| -20| 10|

10| 20| 30| 10| 50|

If specifications are at nominal 100, what you say about the capability of the process? Calculate Cp and Cpk?

Question 8: The thickness of a printed circuit board is an important quality parameter. Data on board thickness (in inches) are given below, for 20 samples of 3 boards each. Sample No.| x1| x2| x3|

1| 0.0629| 0.0636| 0.0640|

2| 0.0630| 0.0631| 0.0622|

3| 0.0628| 0.0631| 0.0633|

4| 0.0634| 0.0630| 0.0631|

5| 0.0619| 0.0628| 0.0630|

6| 0.0613| 0.0629| 0.0634|

7| 0.0630| 0.0639| 0.0625|

8| 0.0628| 0.0627| 0.0622|

9| 0.0623| 0.0626| 0.0633|

10| 0.0631| 0.0631| 0.0633|

11| 0.0635| 0.0630| 0.0638|

12| 0.0623| 0.0630| 0.0630|

13| 0.0635| 0.0631| 0.0630|

14| 0.0645| 0.0640| 0.0631|

15| 0.0622| 0.0644| 0.0632|

16| 0.0631| 0.0627| 0.0630|

17| 0.0616| 0.0623| 0.0631|

18| 0.0630| 0.0630| 0.0626|

19| 0.0636| 0.0631| 0.0629|

20| 0.0640| 0.0635| 0.0629|

Set up X-bar - R charts? Is the process in control?

Question 9: Samples of size 5 are taken every 45 minutes on cigar lighter detent. The following results are obtained. Set up X-bar – R chart and examine the process for statistical control? Sample No.| x1| x2| x3| x4| x5|

1| 1| 3| 4| 3...

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