1. The volume of orange-flavored cordial in bottles follows normal distribution with a mean volume of 758 ml and a standard deviation of 12 ml. A random sample of 10 bottles is taken and the mean volume is calculated.
a. Write down the distribution of the sample mean.
b. Find the probability that the sample mean volume lies between 750 ml and 760 ml.
c. If 25% of the bottles are considered exceeding the limit of the mean volume, what is the maximum mean volume of the bottles required?