The number of trades (in thousands) completed daily by an online stock brokerage follows a normal distribution with a mean of 97.5 and a standard deviation of 25.8. On average, the brokerage receives $8.46 commission per trade.

For samples of sizen =15days:

1. 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 dollars

1. Determine the following probabilities (as percentages) accurate to one (1) decimal place.

What is the probability that the mean daily commissions received is

1. a) more than $739,404?= %
2. %) between $737,712 and $873,918?= %

For the given sample size, what is the maximum average daily commissions receivable from the lowest 7.5% volume trading days?

Round to the nearest thousand dollars.=