I have worked out the answers for both c and d but I am stuck on the final part for sketching a drawing and comparing the results.
Any help would be appreciated.
c) Your analysis shows that the mean capacitance of a batch of 500 of the capacitors you have selected is 46 μF, with a standard deviation of 4 μF. Assuming the capacitors are normally distributed, determine the number of capacitors likely to have values between 42 μF and 50 μF.
Note: Use the z-table given in Appendix A when answering part c.
d) The Quality Assurance Department is anxious to improve the nominal value of the capacitors to ensure more of them fall within the rated tolerance band. The manufacturing process is adjusted in an attempt to bring about this improvement. Following the adjustment, a further sample of 100 capacitors is taken in order to determine if the adjustment has resulted in an improvement to the nominal value of the capacitors. Analysing this second sample, it is noted that the mean value is now 46.5 μF, with a standard deviation of 2 μF.
By comparing these new results of the capacitor values following the manufacturing adjustment, with the values obtained in part (c) recorded before the adjustment, show whether or not you agree with the hypothesis that the adjustment to the manufacturing process has had a beneficial effect by making the capacitor values closer to the desired manufactured nominal value of 47 μF.
Illustrate your answer with a hand drawn sketch of the normal distribution, with shaded regions representing the results of your analysis, which you can show to the Quality Assurance Manager.
Note: Use the z-table given in Appendix A when answering part d.