1. It is known that the incomes of subscribers to a particular magazine have a normal distribution with standard deviation $6800. A random sample of 30 subscribers is taken. a) What is the probability that the sample standard deviation of their incomes is bigger than $4500? b) What is the probability that the sample standard deviation of their incomes is less than $7500?

2. The standard deviation of the diameter of screw-top lids must not be larger than 0.6mm to ensure that the lids will properly fit a certain set of glass jars. A random sample of 15 lids yields a standard deviation of 0.78mm. Conduct the appropriate hypothesis test at the 1% level to determine if to test whether the manufacturing process needs adjusting. The p-value for this test is 0.05. Remember to set up your hypothesis test correctly