c) A batch of 2450 transformers from the production line have a mean output voltage of 215.3 V and the Standard deviation of the output voltage is 2.8 V. If the voltages of the transformers in the box are assumed to be normally distributed, determine the following: i) ii) ii) The number of Transformers with output voltages greater than 216.9 V. The number of Transformers with output voltages less than 213.1 V, The number of Transformers with output voltages between 214 V and 216 V. For this problem you should use the table of z-values shown in Figure 1.

Linear Algebra: A Modern Introduction
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Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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b)

Task 6
The company kave checked the capacitances of a batch 120 of 100 µF capacitors and given
you the results as shown in the group frequenty table 1 below.
Use that data given to calculate the mean and standard deviation of the data.
You shoutd provide clear explanation of the caleutations used and a suitably chosen graphical
-representation of your results suitable for a non-technical audience.
You may use a spreadsheet for these calculations, but you must provide clear
evidence of the formulas used in each cell and submit the spreadsheet file with your
report.
Capacitance values between
(µF)
Class Frequency
94-95.9
7
96-97.9
19
98-99.9
35
100-101.9
31
102-103.9
23
104-105.9
5
b)) The company automatically manufacture its control boards. The quality inspector has
determined that in each package, 89% of the control boards are within the correct tolerance
values with respect to their functionality, the remainder were out of tolerance. If a random
sample of 6 boards are drawn from the package determine the probabilities that:
i)
ii)
ii)
3 of the sample boards are out of tolerance
More than 3 of the sample boards are out of tolerance
Less than three of the sample boards are out of tolerance.
Transcribed Image Text:Task 6 The company kave checked the capacitances of a batch 120 of 100 µF capacitors and given you the results as shown in the group frequenty table 1 below. Use that data given to calculate the mean and standard deviation of the data. You shoutd provide clear explanation of the caleutations used and a suitably chosen graphical -representation of your results suitable for a non-technical audience. You may use a spreadsheet for these calculations, but you must provide clear evidence of the formulas used in each cell and submit the spreadsheet file with your report. Capacitance values between (µF) Class Frequency 94-95.9 7 96-97.9 19 98-99.9 35 100-101.9 31 102-103.9 23 104-105.9 5 b)) The company automatically manufacture its control boards. The quality inspector has determined that in each package, 89% of the control boards are within the correct tolerance values with respect to their functionality, the remainder were out of tolerance. If a random sample of 6 boards are drawn from the package determine the probabilities that: i) ii) ii) 3 of the sample boards are out of tolerance More than 3 of the sample boards are out of tolerance Less than three of the sample boards are out of tolerance.
c)
A batch of 2450 transformers from the production line have a mean output voltage of 215.3 V and
the Standard deviation of the output voltage is 2.8 V. If the voltages of the transformers in the box
are assumed to be normally distributed, determine the following:
i)
ii)
iii)
The number of Transformers with output voltages greater than 216.9 V.
The number of Transformers with output voltages less than 213.1 V,
The number of Transformers with output voltages between 214 V and 216 V.
For this problem you should use the table of z-values shown in Figure 1.
All the calculations must be clearly explained with suitable diagrams where
appropriate to aid understanding to a non-technical audience.
Transcribed Image Text:c) A batch of 2450 transformers from the production line have a mean output voltage of 215.3 V and the Standard deviation of the output voltage is 2.8 V. If the voltages of the transformers in the box are assumed to be normally distributed, determine the following: i) ii) iii) The number of Transformers with output voltages greater than 216.9 V. The number of Transformers with output voltages less than 213.1 V, The number of Transformers with output voltages between 214 V and 216 V. For this problem you should use the table of z-values shown in Figure 1. All the calculations must be clearly explained with suitable diagrams where appropriate to aid understanding to a non-technical audience.
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