The number of trades (in thousands) completed daily by an online stock brokerage follows a normal distribution with a mean of 119.8 and a standard deviation of 27.8. On average, the brokerage receives $7.37 commission per trade. For samples of size n=8n=8 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 = b) Standard deviation =
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 $848,287? % b) between $771,639 and $977,262?
2. For the given sample size, what is the maximum average daily commissions receivable from the lowest 12.5% volume trading days?

Round to the nearest thousand dollars.