Question

can someone please help me solve the problem? A process is known to yield precision circuit breakers with a constant standard deviation of 0.0428 Amps, regardless of the level of mean break current. What mean break current should be aimed for in the process, if it is specified that 2% of break currents may be less than 1Amp, assuming a normal distribution?

Answer 1

When 2% is converted to a decimal fraction it becomes 0.002. Reference to a standard normal distribution table shows that the z-score for a cumulative probability of 0.002 is:\[z=-2.88\]
Using the equation
\[z=\frac{X-\mu}{\sigma}\]
with z = -2.88, X = 1 and sigma = 0.0428, we get
\[-2.88=\frac{1-\mu}{0.0428}\ ..............(1)\]
Now you just need to solve equation (1) to find the value of mu, which is the required mean break current. Can you do that?