The number of trades (in thousands) completed daily by an online stock brokerage follows a normal distribution with a mean of 99.9 and a standard deviation of 29.8. On average, the brokerage receives $6.39 commission per trade. For samples of size n = 15 days: 

Determine the mean and standard deviation of the sampling distribution of the sample mean daily commissions received (in thousand dollars) accurate to 3 decimal places: 

a) Mean = thousand dollars 

b) Standard deviation = thousand dollar

Determine the following probabilities (as percentages) accurate to one (1) decimal place. What is the probability that the mean daily commissions received is 

a) less than $596,187? % 

b) between $595,548 and $739,962? % For the given sample size, what is the maximum average daily commissions receivable from the lowest 12.5% volume trading days?