Homework 12, Due W 03/21
Read Chapter 3, Chapter 13: Pages 334-336.
Problems to be turned in: Show all working. Answers without explana-
tion will not get any credit.
1. Ex. 3.29
2. Ex. 3.30
3. Ex. 3.44
4. Ex. 3.46
5. Ex. 3.50
6. In a certain class, there was an exam out of 100. The mean score was 80.
The professor picked a student at random and announced his/her score. Call
it X. Assume Xhas Binomial distribution.
To view this as a Binomial Model, note that the exam carried 100 points, and
for each point the student could either get 1 (success) or 0 (failiure). Then
the student’s total score, Xcounts the total number of successes. Assuming
that the chance of success was the same for each point, Xhas Binomial dis-
tribution with n= 100 and p= 0.8.
Use this information to answer the following questions:
a) What is the probability that the randomly picked student got 100.
b) What is the probability that the student got an A? Use Normal
Approximation to Binomial (see Page 336) to find the probability.
c) How much should the student score to be in the top 5% of the class?
Again use Normal Approximation to find the answer.
d) Figure 1 shows the histogram of the score distribution for the class.
Comment on the shape of the histogram. Is Binomial distribution a good
assumption?
1
