Probability

Scenario: Suppose that the amount of credit card debt for college seniors is normally distributed with an average debt of $3262 and a standard deviation of $1100.

1. What is the probability that a randomly chosen college senior owes no more than $1000?
2. What is the probability that a randomly chosen college senior owes at least $4000?
3. What is the probability that a randomly chosen college senior owes between $3000 and $4000?
4. Find the quartiles (Q1 and Q3) for the distribution of credit card debt for college seniors. (Hint: Think about the percentages that are associated with each quartile. These percentages correspond to area.)

PART 2

In this part we are going to work with the Uniform distribution (a=0, b=2) and sample from it in order to generate a sampling distribution of the mean.

5. Assume X is a randomly chosen number between 0 and 2. That means that X is Uniformly distributed with a=0 and b=2. Below calculate the mean and standard deviation for X.

μX=

σX =

6. On a new sheet in Excel you are going to generate 25 random samples of size n=100. Each sample is taken from the Uniform distribution described above. To do this:
   • Go to DataData AnalysisRandom Number Generation. Enter the values shown on the screenshot below and then click OK

Sample Solution