I\'m having problems with a couple of my hw problems.... A chemical plant superi

Question

I'm having problems with a couple of my hw problems....
A chemical plant superintendent orders a process shutdown andsetting readjustment whenever the pH of the final product fallsbelow 6.90 or above 7.10. The sample pH is normallydistributed with unknown , and standard deviation of0.05. Determine the probability:
a) of readjusting when the process is operating as intendedand =7.0 b) of readjusting when the process is slightly off target andthe mean pH is =7.02 c) of failing to readjust when the process is too alkaline andthe mean pH is =7.15 d) of failing to readjust when the process is too acidic andthe mean pH is =6.80
Thanks!
A chemical plant superintendent orders a process shutdown andsetting readjustment whenever the pH of the final product fallsbelow 6.90 or above 7.10. The sample pH is normallydistributed with unknown , and standard deviation of0.05. Determine the probability:
a) of readjusting when the process is operating as intendedand =7.0 b) of readjusting when the process is slightly off target andthe mean pH is =7.02 c) of failing to readjust when the process is too alkaline andthe mean pH is =7.15 d) of failing to readjust when the process is too acidic andthe mean pH is =6.80
Thanks!

Explanation / Answer

(a) P(X7.1) =P(X7.1) =P((X-)/ (7.1-7)/0.05) =P(Z2) =0.0228+0.0228 (check normal table) =0.0556

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