The number of trades (in thousands) completed daily by an online stock brokerage follows a normal distribution with a mean of 90.3 and a standard deviation of 26. On average, the brokerage receives $8.82 commission per trade. For samples of size n=11 days

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
2. 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 $723,240? %% b) between $677,376 and $911,106? %%
2. For the given sample size, what is the minimum average daily commissions receivable from the highest 5.5% volume trading days?

Round to the nearest thousand dollars.