Math 1115 Assignment 2-Due date June 29th 1- An experiment is designed to study the effect of calcium and vitamin D supplements on the bones of first-year college students. The outcome measure is the total body bone mineral content (TBBMC), a measure of bone health. Three doses of calcium will be used: 0, 200 and 400 milligrams per day. The doses of vitamin D will be 0, 50 and 100 units per day. The calcium and vitamin D will be given in a single tablet. All tablets, including those with no calcium and no vitamin D, will look identical. Subjects for the study will be 90 men and 90 women. a) What are the factors and treatments for this experiment? b) How would you randomize the 180 college students? c) Is there a placebo in this experiment? Explain your answer. 2- What's wrong? State what is wrong in each of the following scenarios? a) A parameter describes a sample. b) Bias and variability are two names of the same thing. c) Large samples are always better than small samples. d) A sampling distribution is something generated by a computer. 3- On a recent holiday evening, a sample of 500 drivers was stopped by the police. Three hundred were under 30 years of age. A total of 250 were under the influence of alcohol. Of the drivers under 30 years of age, 200 were under the influence of alcohol. Let A be the event that a driver is under the influence of alcohol. Let Y be the event that a driver is less than 30 years old. a. Determine P(A) and P(Y). b. Draw a tree diagram for this problem. c. What is the probability that a driver is under 30 and not under the influence of alcohol? d. Given that a driver is not under 30, what is the probability that he/she is under the influence of alcohol? e. What is the probability that a driver is under the influence of alcohol if we know the driver is under 30? f. Are A and Y mutually exclusive events? Explain. g. Are A and Y independent events? Explain. 4- A fair six-sided die is tossed. You win $2 if the result is \"1\