Question: (8 points) Daily fluctuations in the prices of precious metals such as gold have been empirically shown to be well approximated by a normal distribution when monitored over short intervals of time. In August 2007, the daily price of gold (1 troy ounce) was believed to have a mean of $720.00 and a standard deviation of $24.00. A young broker, working under these assumptions, is interested in finding the probability that the price of gold the next day would be:

a. Between $680.00 and $745.00?

b. Greater than $755.00?

c. Less than $690.00?

d. Greater than $705.00 or less than $745.00?

e. Suppose the standard deviation is unknown, but there is a 95% chance that the price would be more than $665.00. What would be the value of the standard deviation? Assume the average is still $720.00.

f. Suppose the mean value is unknown, but the standard deviation is still $16.00. How much would the average price of gold per ounce be if there is an 80% chance the price would be less than $760.00?