Revisit Bryden’s sock drawer from earlier in the test (4 Cool socks, 6 Hunk socks, 2 Genius socks). If Mr. Smith draws out two socks, one at a time for Bryden to wear, what is the probability that they do not match?  

The probability that a student graduating from West Texas A&M University has student loans to pay off after graduation is 0.60. If two students are randomly selected from this university, what is the probability (rounded to the nearest two decimal places) that neither of them has student loans to pay off after graduation?

The following table gives the frequency distribution of the number of telephones owned by a sample of 50 households selected from a city.

Number of Telephones Owned   Frequency (f)
0   3
1   20
2   14
3   3
4   10
The relative frequency of the first class, rounded to two decimal places, is:

The temperatures (in degrees Fahrenheit) observed during selected seven days of summer in Los Angeles are:

78 99 68 91 105 75 85

The standard deviation, rounded to two decimal places, of these temperatures is:

The ages of all high school teachers in New York state have a bell-shaped distribution with a mean of 39 years and a standard deviation of 7 years. According to the empirical rule, the percentage of teachers in this state who are 32 to 46 years old is approximately:

The waiting times (in minutes) for 11 customers at a supermarket are:

14 9 15 4 4 7 9 11 14 2 6

The percentile rank for the customer who waited 11 minutes is 64%. Give a brief interpretation of this percentile rank.

Consider the following data for two variables, x and y.

a. Compute the standardized residuals for these data.

Problem 10-15

Island Airlines Inc. needs to replace a short-haul commuter plane on one of its busier routes. Two aircraft are on the market that satisfy the general requirements of the route. One is more expensive than the other but has better fuel efficiency and load-bearing characteristics, which result in better long-term profitability. The useful life of both planes is expected to be about seven years, after which time both are assumed to have no value. Cash flow projections for the two aircraft follow.

1. Calculate the payback period for each plane and select the best choice. Round your answers to one decimal place.

   Low Cost	years
   High Cost	years

   
   
2. Calculate the IRR for each plane and select the best option. Use the fact that all the inflows can be represented by an annuity. Round your answers to one decimal place.

   Low Cost	%
   High Cost	%

   
   IRR also selects the   cost plane.
   
3. Compare the results of parts (a) and (b). Both should select the same option, but does one method result in a clearer choice than the other based on the relative sizes of the two payback periods versus the relative sizes of the two IRRs?
   The input in the box below will not be graded, but may be reviewed and considered by your instructor.
   
   
4. Calculate the NPV and PI of each project assuming a cost of capital of 8%. Use annuity methods. Do not round intermediate calculations. Round PVFA values in intermediate calculations to four decimal places. Round NPV to the nearest dollar, round PI to two decimal places.

   	Low Cost	High Cost
   NPV	$	$
   PI

   
   Which plane is selected by NPV?
     cost plane.
   By PI?
     cost plane.
   
5. Calculate the NPV and PI of each project, assuming the following costs of capital: 2%, 4%, 6%, 8%, and 10%. Use annuity methods. Do not round intermediate calculations. Round PVFA values in intermediate calculations to four decimal places. Round NPV to the nearest dollar, round PI to two decimal places. Use a minus sign to indicate a negative NPV.

   		Low Cost	High Cost
   2%	NPV	$	$
   	PI
   4%	NPV	$	$
   	PI
   6%	NPV	$	$
   	PI
   8%	NPV	$	$
   	PI
   10%	NPV	$	$
   	PI

   
   Is the same plane selected by NPV and PI at every level of cost of capital? Investigate the relative attractiveness of the two planes under each method.
   

Accidental Death & Dismemberment Insurance covers accidents that results in death or loss of limbs due to accidents. Considering dismemberments only, let a discrete random variable X be the number of limbs lost from a policy holder in a given year.

Suppose that the probability distribution of X is x

0 p(x)=0.80

1 p(x)=0.13

2 p(x)=0.04

3 p(x)=0.02

4 p(x)=0.01

(a) Find the expected number of limbs lost for a randomly selected policy holder in a given year.

(b) suppose the insurance company pays $10,000 for loss of one limb, $20,000 for loss of two limbs, $50,000 for loss of three limbs, and $100,000 for loss of all limbs, how much should the annual premium be if the insurance company wants an average of $50 profit per policy holder? Hint: What is the expected insurance payment for an arbitrary policy holder?

Paulson is in charge of a project at the local community center. The center needs to remodel one of the rooms in time for the start of a new program. Delays in the project mean that the center must rent other space at a nearby church at additional cost (and Paulson gets a roasting).
Time and cost data for your project are contained in Table below. Paulson’s interest is in minimizing the cost of the project to the community center.

TABLE
DATA FOR THE COMMUNITY CENTER PROJECT
Activity
Normal Time (days)
Normal Cost($)
Crash Time (days)
Crash Cost ($)
Immediate Predecessor(s)
START
0
0
0
0
-
A
10
50
8
150
START
B
4
40
2
200
START
C
7
70
6
160
B
D
2
20
1
50
A, C
E
3
30
3
30
A, C
F
8
80
5
290
B
G
5
50
4
180
D
H
6
60
3
180
E, F
FINISH
0
0
0
0
G, H

a. Using the normal times for each activity, what is the earliest date Paulson can complete the project?

b. Suppose the variable overhead costs are $50 per day for your project. Also, suppose that the center must pay $40 per day for a temporary room on day 15 or beyond. Find the minimum-cost project schedule (best chance that Paulson is not hauled by Church authorities). What is the minimum cost? (3+7 = 10 Marks)

Apple computer is a highly vertically integrated company. The design of products like the iPad is done by a division of Apple, while another division runs retail outlets to sell them directly to consumers. Use concepts from class the advantages and disadvantages of Apple being vertically integrated in this fashion.

A 4.0 ? diameter merry-go-round (mass 270 ??) is spinning at 15 ???. A child of 35.0 ?? runs tangent to the merry-go-round at 3.0 ?/?, in the same direction that it is turning, and jumps onto the outer edge. Calculate the merry-go-round’s angular velocity, immediately after the child jumps on.

The morley dataset can be seen as a randomized block experiment with Run as the treatment factor and Expt as the blocking factor. Is there a difference between runs and what efficiency is gained by blocking?

Please solve using R. morley is a dataset in R. To access this dataset use:

library(faraway)

attach(morely)

A 1200-kg car is travelling east at a rate of 9 m/s. A 1600-kg truck is travelling south at a rate of 13 m/s. The truck accidentally runs a stop sign and collides with the car in a completely inelastic collision. What is the speed of the combined mass after the collision?