9. Penicillin is produced by the penicillium fungus, which is grown in a broth whose sugar content must be carefully controlled. The optimum sugar concentration is 4.9mg/ml. if the concentration exceeds
6.Omg/ml, the fungus dies and the process must be shut down for the day. A supplier has got broth
X that is normally distributed with mean 5.2 mg/ml and standard deviation 0.4mg/ml. Broth Y is
normally distributed with mean 4.9mg/ml with variance 0.36mg/ml?.
a) Calculate the proportion of days for which the process will shut down for both broth X and broth
Y
b) Make a recommendation to your manager as to which broth should be bought