Business Finance Homework Help

This week, we are going to use the Central Limit Theorem. We are going to pretend that our data set represents the entire population of ABC Company. It doesn’t, but we are going to pretend that it does.

1. What is the mean dollar amount that is recommended by the population of employees?

2. Now, we are going take 3 samples of 10 dollar amounts from the spreadsheet and average (find the mean of) them. Open the spreadsheet and make sure you are on the Week 4 tab.

Go to the random number generator at https://www.google.com/search?q=random+number+generator&oq=random+number&aqs=chrome.0.0j69i57j0l6.3428j0j7&sourceid=chrome&ie=UTF-8

(or any other random number generator)

Put in the minimum number of 5 (this aligns with the cell that begins your list of numbers).

Put in the maximum number of 56 (this aligns with the cell that ends your list of numbers).

Hit “generate.”

The number given tells you what cell to go to. For example, if I got a 48 on the random number generator, I would put my cursor in cell 48 and record the number that is there. For example, if there were a “75” in that cell on the Excel spreadsheet, I would write down 75. Continue to hit the random number generator 9 more times. Record the other 9 values in the cells. Do not worry about repeats. Provide your list of the 10 values from the cells.

Average (find the mean of) those ten values. Write down your sample mean.

Repeat this exercise two more times. You will have a total of three sample means.

3. Comment on your three means of the samples. Were they the same? How did they compare to the mean of the population? Were the samples representative of the population? Why or why not?

4. If you took your 3 sample means and gathered the 3 sample means from all your classmates and put them on a histogram, what should the shape of that histogram be? Why? How does this relate to the Central Limit Theorem?

Week 4 Assignment

1.What two properties must be satisfied by a continuous probability distribution / probability curve?

2.Explain what the mean µ tells us about a normal curve, and explain what the standard deviation σ tells us about a normal curve.

3.Explain how to compute the z value. What does the z value tell us about the value of the random variable?

4.Let x be a normally distributed random variable with µ=30 and σ=5. Find the z value for each of the following observed values of x:

a.X = 25

b.X = 15

c.X = 30

d.X = 40

e.X = 50

5.If the random variable z has a standard normal distribution, sketch and find each of the following probabilities.

a.P( 0 < z <1.5)

b.P( z > 2)

c.P( z < 1.7)

d.P( z < -1.6)

6.Weekly demand at a grocery store for a brand of breakfast cereal is normally distributed with a mean of 800 boxes and a standard deviation of 75 boxes. What is the probability that the weekly demand is:

a.960 boxes or less?

b.More than 1005 boxes?

c.Between 750 and 850 boxes?

7.What does the Central Limit Theorem tell us about the sampling distribution and sample mean?

8.In each of the following cases, determine whether the sample size n is large enough to say that the sampling distribution of p (p hat) is a normal distribution.

a.P=0.4; n=100

b.P=0.1; n=10

c.P=0.1, n=50