1. The women and Children's hospital has a lab which is heavily secured as it contains many animals for scientific testing. In a particular lab, there are two sets of genetically identical mice (type A and type B). Of these mice, 35% are type B. Half of the type A mice have been infected with osteomylitis. Only a quarter of the type B mice have been infected. The cleaning lady wanted to clean out the cages and put all the mice in a single cage.
a) You select a mouse randomly. What is the probability that it is a type A mouse with osteomylitis?
b) What is the probability that a mouse selected at random does not have osteomylitis?
d) Are the events Type A and Has Disease independent? (iustifv)
c) Three mice were selected at random. What is the probability that at least one of them is type A?
2. A forensics researcher investigating a crime scene must collect blood samples left at the crime scene (the culprit has left the scene). Among other things she wishes to identify if any alcohol had been consumed prior to the crime. Alcohol is not distributed evenly through the circulatory system. The amount of alcohol found in blood samples follows a Normal distribution. For the individual in question, the mean alcohol level is 0.076 with standard deviation 0.018. The investigator gets 12 samples of blood.
a. What is the model for the sample mean? Be sure to specify the parameters and to justify your answer.