Problem-12

A soft drink machine is regulated so that the amount of drink it dispenses follows a normal distribution with a known standard deviation of the drinks dispensed of 20 milliliters.

A random sample of 30 drinks from the machine had an average volume of 373 milliliters. Determine a 95% confidence interval for the average amount of all drinks dispensed by this machine.

Problem-13

A soft drink machine is regulated so that the amount of drink it dispenses follows a normal distribution with a known standard deviation, and it is believed that standard deviation of the drinks dispensed is 20 milliliters.

However a random sample of 30 drinks from the machine produced an average value of 373 milliliters and standard deviation of 23.4 milliliters; therefore, based on the results from sample data, there is concern that population standard deviation might be higher than what is believed.

Check the validity of the concern by determining a 95% confidence interval for the standard deviation of all drinks dispensed by this machine.