Homework Answers

3. Professor Brown has been teaching the same university psychology course for many years, and she has been keeping a record of all the grades given to the students. Suppose that her student’s grades follow a normal distribution, with an average of 70 and a standard deviation of 12.

(a) Suppose you will be taking her class next semester. What is the probability that you will get a grade between 70 and 85?

(b) What minimum grade do you need in order to qualify for Professor Brown’s Honour Roll, which is reserved for the top 8% of students?

(c) Suppose this professor will have a group of 25 students next semester. What is the probability that her class average will not be between 65 and 75?

Advanced QM

1. In the past year, Gino’s Pizza Restaurant was profitable on exactly 75% of its business days. During the next 8 business days, what is the probability that Gino’s will be profitable for:

(a) exactly 6 days?

(b) less than 7 days?

2. An insurance company says that 15% of all fires are caused by arson. A random sample of 50 fire insurance claims are under study. Let r be the number of fires that were really started by arson in this sample.

(a) What is the expected number (mean) of arson fires among these 50 fires?

(b) What is the standard deviation of the number of arson fires?

Find all the values of k so that the set{ ( 1,−3,2),(−3,9,−6),(5,−7,k)} form the basis for R³