# 1. the probability that house sales will increase in the next

1. The probability that house sales will increase in the next 6 months is estimated to be 0.25. The probability that the interest rates on housing loans will go up in the same period is estimated to be 0.74. The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89. The probability that house sales do not increase AND interest rates do not increase during the next 6 months is

a) 0.11 b) 0.26 c) 0.45 d) 0.64 e) 0.15 f) 0.10

2. Suppose each sample of air has a 10% chance of containing a particular rare molecule. Find the probability that, in a collection of 20 independent samples, at least one sample contains the rare molecule.

a) 0.555 b) 0.440 c) 0.878 d) 0.265 e) 0.098

3. Two assets have variances of 24 (asset A) and 16 (asset B). The covariance between them is -10. If a portfolio is composed of the two assets in the proportions 60% in A and 40% in B the portfolio standard deviation will be:

a) 14.4 b) 2.19 c) 4.8 d) 2.53 e) 6.4

4. Its time to create a contract for football running back Reggie Bush for the New England Patriots. The Patriots offer him the following incentive package:

Rush for 0 to 900 yards in 2015, earn a bonus of $0

Rush for over 900 and up to 1500 yards, earn a bonus of $500,000

Rush for over 1500 yards, earn a bonus of $1,000,000

Assuming that his rushing performance follows a normal distribution with a mean of 750 yards and a standard deviation of 320 yards, what is his expected bonus to be paid? [the answers are rounded so choose the closest answer to what you calculate].

a) $321,000 b) $350,000 c) $227,000 d) $303,000 e) $275,000

5. The scatterplot below shows heights (x) and weights (y) for 126 college students. The equation for the regression line was given as yhat = -200+5x. What is the predicted weight for a college student who is 65 inches tall?

a) 120 b) 155 c) 160 d) 170 e) 125

6. The car speeds that Trooper Tracy clocks along a stretch of I85 are normally distributed with a mean of 67 mph and a standard deviation of 9 mph. Tracy only gives tickets to cars in the upper 10% of the speed distribution. What is the maximum speed you can drive to make sure you don’t get a ticket?

a) 76.33 b) 78.52 c) 74.57 d) 81.80 e) 79.65

7. Consider the following profit table for a company’s decision for a piece of equipment.

If P(High) is 0.2, P(moderate) is 0.5, and P(low) is 0.3, the optimal alternative to maximize expected monetary value would be:

A) Buy B) Rent C) Lease D) High E) Moderate F) Low

8. On a Stat 100 test, the middle 95% of students score between 46 and 82. Assume the scores have a normal distribution. Calculate the mean score and the standard deviation of the scores. In the choices below, the mean is given first in each case, and then the standard deviation (we rounded the standard deviation).

a) 64, 18 b) 64, 32 c) 18, 32 d) 18, 23 e) 64, 9

9. Buddy works Monday through Friday and is consistently late for work. His boss has decided he will give him a warning every work day he is late next week. On any given work day, the probability that Buddy is on time is 35%. Assume each day’s outcome (late/on-time) is independent. Suppose, instead of a warning, the boss has decided he will deduct $3.50 from Buddy’s pay check each day he fails to be on time next week. What is the expected value and variance for the amount of money Buddy will lose next week? Write your answers in the boxes below and show your work under the boxes.

Expected Value =

Variance =

10. Let data set X represent the numbers 1,2,3,4,5,6,7,8,9,10. Let Y=1+5X, and let W=X+Y. Fill in the missing values from the Stata output. No extensive hand calculations are required. [write answers in box for clarity-show any work for credit].

a) Standard deviation of Y is

b) Covariance of X and Y is

c) Variance of W is

11. For any given day of the week, let X be the number of meals you eat in the dining hall, and Y be the number of meals your roommate eats. The joint probability distribution of the number of meals you and your roommate eat at the dining hall for any given day is shown below:

a) What is the probability that you will eat an even number of meals and your roommate eats an odd number of meals?

X= # of meals you eat

Y=# of meals your roommate eats

X=1 X=2 X=3

Y=1 0.06 0.1 0.02

Y=2 0.1 0.3 0.1

Y=3 0.02 0.1 0.2

b) Given your roommate eats 3 meals, what is the probability you eat 1 meal?

c) Are X and Y independent? Be sure to show your work.

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