Stat 1 Spring 2011 Assignment 9 - due Tuesday, April 12

SCC problems: 20.8, 20.10, 20.12, 20.15, 20.16

Additional Problems:

1. If you roll a 6-sided die 5 times, what is the probability you will
roll at least one 6?

2. Suppose 10 students each flip 100 coins and construct a 95% 
confidence interval for p, the probability that the coin lands heads. If 
the coins are all fair (so p=0.5) what is the probability that at least one 
of the ten intervals will not contain 0.5? Hint: By construction, the probability 
is 0.95 that any one of the intervals will contain 0.5. 

3. (2 pts)  Here are the counts (in thousands) of earned degrees in the 
U.S. in a recent year, classified by level and by the gender of the degree 
recipient:

			female		male	
Bachelor's		616		529	
Master's 		194		171	
Professional		 30		 44	
Doctorate		 16		 26	
------------------------------------------------------
total			856		770 

Imagine choosing a degree recipient at random.

a) What is the probability that the person you choose is female?

b) If you choose a person who received a professional degree, what 
is the conditional probability that you chose a female?

c) If you choose a female,  what is the conditional probability that 
you chose a professional degree recipient?

d) Are the events "choose a female" and "choose a professional degree 
recipient" disjoint? Are they independent? Explain you know.

4) Suppose a test for Lyme disease is positive with probability 
0.9 if a person has Lyme disease, and with probability 0.05 if they do not. 
If a person is bitten by a deer tick, the CDC says the probability of 
getting Lyme is about 0.01. If a person bitten by a deer tick tests 
positive, what is the conditional probability that they have Lyme? Hint: 
construct a table of 100 people who obey these probabilities exactly. 
Alternately, you could make a tree that splits first on Lyme or No Lyme, 
and then on Positive and Negative.