question 1

A population of values has an unknown distribution with =63.7=63.7 and =18.4=18.4. You intend to draw a random sample of size n=191n=191. What is the mean of the distribution of sample means? x=x= __________________(Please enter an exact answer.) What is the standard deviation of the distribution of sample means? x=x= ______________ (Please report your answer accurate to 2 decimal places.)

question 2

A population of values has a normal distribution with =140.7=140.7 and =5.6=5.6. You intend to draw a random sample of size n=11n=11.

First calculate zz, round it to two (2) decimal places, then use the rounded zz-score to determine the required probability accurate to four (4) decimal places.

1. Find the probability that a single randomly selected value is greater than 144.1. P(x>144.1)=P(x>144.1)= __________
2. Find the probability that a sample of size n=11n=11 is randomly selected with a mean greater than 144.1. P(x>144.1)=P(x>144.1)= ____________

Question 3

The number of trades (in thousands) completed daily by an online stock brokerage follows a normal distribution with a mean of 103.2 and a standard deviation of 26.5. On average, the brokerage receives $7.73 commission per trade. For samples of size n=18n=18 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) less than $784,595? %________% b) between $732,804 and $906,729? %__________%
2. For the given sample size, what is the minimum average daily commissions receivable from the highest 20% volume trading days?

Round to the nearest thousand dollars. ________