Fit to page Page view A Read aloud Add notes 1. Drug lots produced by pharmaceutical companies are subject to very strict regulations and controls by the U.S. Food an Drug Administration (FDA). Pharmamed is a pharmaceutical company that recently started experimentation for a new drug. The concentration of the active principle in a lot of this drug has a mean of 98mg with a standard deviation of 1.3mg. For a lot of this drug to pass FDA inspection, the concentration of active principle cannot be lower than 96mg or higher than 99mg. In the last FDA inspection, 71.7% of the lots produced by Pharmamed passed the inspection. (a) Based only on the above information, are there any reasons to doubt whether or not the concentration of active principle in the lots is normally distributed? Explain why or why not. [2 marks] For parts (b), (c) and (d), we will make the assumption that the concentration of active principle in the lots follows a normal distribution with the mean and standard deviation values given above. (b) If 4 lots are sampled out of the lots produced by Pharmamed, what is the approximate probability that the average concentration of active principle in the 4 lots does not meet the FDA requirements? Clearly state what assumptions are necessary in order for this probability calculation to be possible. [3 marks] (c) If 40 lots are sampled out of the lots produced by Pharmamed, what is the probability that 28 or more lots pass FDA inspection? Clearly state what assumptions are necessary in order for this probability calculation to be possible. [3 marks] (d) A lot is made up of several tablets of the same drug. In the previous questions we assumed that an inspection analysed all tablets in a lot. However, tablets that are inspected cannot be sold on the market because they are destroyed in the process. Therefore, the FDA conducts the analysis only by looking at a sample of tablets from a lot. If you know that a lot contains a total of 100 tablets and an inspection uses 10 tablets sampled randomly, how would your answers in b and c change? (Hint: assume the distribution of the concentration of active principle is the distribution of the sample average of the 100 tablets.) [6 marks]