Assignment #5

## Problem #1: (6)

You are a high-school basketball coach and the final game of the season is on the line. You must pick one of the following two players to make 3 free-throw attempts. Here are the current season’s outputs for your two best shooters, Lauren and Lisa. Which one is most likely to give you your best result?  Be sure to explain why.

 Lauren 0 1 2 3 Prob. 0.3 0.2 0.2 0.3

 Cappie 0 1 2 3 Prob. 0.1 0.4 0.3 0.2

## Problem #2: (4/4)

You ask your graduate student to roll a die 10,000 times and record the results. Give the expected mean and standard deviation of the outcome. Part B: The die roll experiment is repeated (though with a different graduate student – for some reason your previous student went to work with a different advisor). However in this case, the die is weighted so that a 6 shows up 25% of the time and all remaining numbers show up 15% of the time. Now what is the mean and sd of 10,000 rolls?

## Problem #3: (6)

In a recent year, the Internal Revenue Service received 142,978,806 individual tax returns. Of these, 17,993,498 reported an adjusted gross income of at least \$100,000, and 392,220 reported at least \$1

million. If you know that a randomly chosen return shows an income of \$100,000 or more, what is the conditional probability that the income is at least \$1 million?

## Problem #4: (2/3/3)

In a college population, students are classified by gender and whether or not they are frequent binge drinkers. Here are the probabilities:

 Men Women Binge Drinker 0.11 0.12 Not Binge Drinker 0.32 0.45

(a) Find the probability that a randomly selected student is a male binge drinker, and find the probability that a randomly selected student is a female binge drinker.

(b) Find the probability that a student is a binge drinker, given that the student is male and find the probability that a student is a binge drinker, given that the student is female.

(c) Your answer for part (a) gives a higher probability for females, while your answer for part (b) gives a higher probability for males. Interpret your answers in terms of the question of whether there are gender differences in binge-drinking behavior. Decide which comparison you prefer and explain the reasons for your preference.

## Problem #5: (3/3)

We have now learned two different versions of the addition rule and multiplication rule.

a)      For each of these, explain what the “newer” of ‘General’ version of the rule is saying; that is, what makes it different from the “older” version.  (This explanation does not to be long).

b)      Then explain why the General Addition rule can be applied to both disjoint and non-disjoint situations, and why the General Multiplication rule can be applied to both independent and non-independent situations.

## Problem #6: (6)

Call a household prosperous if its income exceeds \$100,000. Call the household educated if the householder completed college. Select an American household at random, and let A be the event that the selected household is prosperous and B the event that it is educated. According to the Current Population Survey, P(A) = 0.138, P(B) = 0.261, and the probability that a household is both prosperous and educated is P(A and B) = 0.082. What is the probability P(A or B) that the household selected is either prosperous or educated?