PROBLEM 3

• You must use normal graphs from our notes to solve these problems.
• You should be able to look at our notes, draws the normal graphs, use the z-tables and solve the problems.
• Showing your Excel formula is NOT showing your work. If I need to look at an Excel spreadsheet or your output from Excel you are NOT DOING THIS PROBLEM CORRECTLY.
• YOU DO NOT NEED EXCEL TO SOLVE THESE PROBLEMS. IF YOU CHOOSE TO USE EXCEL, USE IT TO CHECK YOUR WORK ONLY!!
  1. What is the probability their annual income is more than $45,500?

The annual income for a sample of 500 part-time students is normally distributed with a mean income of $49,000 and a standard deviation of $3,100.

1. What is the probability their annual income is $51,250-$58,350?
2. What is the probability their annual income is $55,000?
3. How much does a student need to make to be in the bottom 28% for their annual income?

PROBLEM 4

For the following distribution:

x	P(x)
0	0.15
1	0.26
2	0.31
3	0.1
4	0.18

a. Is this a valid probability distribution? Explain.

b. What is the expected value?

c. What is the variance of the distribution?

d.What is the probability that x is more than 2?

Let A be the event X is odd. LetB be the event X is more than 2.

e. Are A and B mutually exclusive? Are they independent?

f. If you know we select an odd number, what is the probability X is more than 2?

g.Compute the probability of the intersection for A and B.

h.Compute the probability of the union for A and B.