a. A standardized test is given to a group of students. Test
scores may range from 0 to 100. Based on statistical data from
a large population, the mean test score is 80 while the most
likely (mode) score is 90. What continuous probability distribution
can be used to model test scores for this situation? Give parameters
for the distribution.
b. The test of part a is to be given to a group of thirty students.
We will average the scores to obtain a class average. What distribution
approximately models the class average? What are its parameters?
c. A professor always gives tests made up of 20 short answer
questions. All the questions give 5 points credit for a total
score of 100 if all are answered correctly. She does give partial
credit. Based on your current capability you judge that your
credit on each question is a random variable with mean equal
to 3 and a standard deviation equal to 1. Assume the questions
are independent in terms of chance of success. Before you take
the test what is your estimate of the mean and standard deviation
of your test score? If a score of 80 or more earns at least
a B, what is the probability that you will earn a B for this
exam? You will have to make an approximation to answer this
question.
d. A professor always gives tests made up of 20 short answer
questions. All the questions give 5 points credit for a total
score of 100 if all are answered correctly. She grades the questions
as either right or wrong with no partial credit. Based on your
current capability you judge that you have a 0.7 probability
of answering any one question correctly. Assume the questions
are independent in terms of chance of success. If a score of
80 or more earns at least a B, what is the probability that
you will earn at least a B for this exam?
