The outlet stream of a continuous chemical reactor is sampled every thirty minutes and titrated. Extensive records of normal operation show the concentration of component A in this stream is approximately normally distributed with mean 41.2 g/L and standard deviation 0.90 g/L.

a) What is the probability that the concentration of component A in this stream will be more than 42.3 g/L?

b) Five determinations of concentration of component A are made. If the mean of these five concentrations is more than 42.3 g/L, action is taken. What is the level of significance associated with this test?

c) State the null hypothesis and the alternative hypothesis that fit the test described in part (b).

d) The test in part (b) is applied. Now suppose the true mean has changed to 43.5 g/L with no change in standard deviation. What is the probability of a Type II error?