Recall the airplane cargo problem we have discussed in our first lecture. An air-freight company has 8 adjacent positions on its Boeing-727 aircraft for freight containers. The weights of this containers depend on what they are carrying. and company statistics indicate that %7 of the containers are classified as ”heavy”. While heavy containers are not inherently dangerous, having two such containers next to each other is considered dangerous should the plane encounter a wind gust.

Understandably, company wants to know how often will it be in a situation where two heavy cargo are next to each other, given that it loads the cargo in a random fashion. One of the engineers claim that this scenario is very unlikely, since chances of loading a single heavy crate is low (%7) and hence having two such containers next to each other is a very low chance event. Is the engineer right? Discuss using random variables and probabilities

The National Overnight (NatO) company provides express small package delivery overnight. Airplanes arrive 24 hours a day at the national hub in Dallas where their contents are unloaded onto cargo vans each capable of holding 1,000 packages. The cargo vans transport the packages to the sorting center. The sorting center has a large storage area designed to hold up to 50,000 packages. After being sorted, another fleet of cargo vans transports the packages to the outgoing planes. However, the following information details the receiving process only. During the night (6 p.m. to 6 a.m.), airplanes arrive at a high rate providing a continuous arrival flow of packages with an average rate of 25,000 packages per hour. However, during the day (6 a.m. to 6 p.m.) air landings are less frequent, resulting in an average arrival rate of 5,000 packages per hour. NatO runs two 12-hour shifts at the sorting center: the night shift starts at 8 p.m. and leaves by 8 a.m. The night shift has the largest number of employees and can process up to 21,000 packages per hour. The day shift, on the other hand, is smaller and can process up to 12,000 packages per hour from 8 a.m. to 8 p.m. It is known that the cargo vans typically had to wait to unload at the sorting center during some portions of the night shift. Cargo van drivers were paid $10/hour, benefits included. NatO begins each night with completely empty storage bins at 6 p.m. Cargo vans begin waiting as soon as the storage area is full. What is the maximum number of cargo vans waiting in line at any given during a 24-hour period? Input your answer as a whole integer such as "17" or "9". If capacity is such that no vans ever have to wait then input "0".

a. Expected Return: Discrete Distribution

A stock's return has the following distribution:

Calculate the standard deviation. Round your answer to nearest two decimal places.

b. The market and Stock J have the following probability distributions:

Calculate the standard deviation for the market and Stock J. Round your answer to nearest two decimal places.

Bob is working as a consultant at Wolf Lamp LLP in British Columbia, Canada. Bob has a temporary workstation set up with a computer, calculator, printer, telephone and scanner. When working on specific projects Bob sometimes ends up bringing some specialized tools with him. He usually starts work around 8:30-9:00am Monday-Friday. He can come in and leave anytime he just must be working from 9-4 Monday-Friday. He gets 2 weeks off a year and 10 sick days. Bob will sometimes bring his work home for his wife to assist him with when he gets too much work at the office, she is also a trained CPA. Bob and his wife love that Bob gets to work for Wolf Lamp LLP as he is paid very well. The one downfall is that if the specific consulting work, he does runs out, they may let him go.

a) Please determine if Bob would be considered an employee or a contractor for tax purposes?

b) Please explain, in your own words, why it matters if Bob is an employee or contractor for tax purposes?

4. Diversification can eliminate risk if two events are perfectly negatively correlated. Suppose that two firms are competing for a government contract and have an equal chance of winning. Because only one firm can win, the other must lose, so the two events are perfectly negatively correlated. You can buy a share of stock in either firm for $20. The stock of the firm that wins the contract will worth $40, while the stock of the loser will worth $10. • If you buy two shares of one firm, calculate the expected value and variance of two shares. • If you buy one share on each firm, calculate the expected value and variance of two shares.

A survey was conducted to determine whether hours of sleep per night are independent of age. A sample of individuals was asked to indicate the number of hours of sleep per night with categorical options: fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8 hours or more. Later in the survey, the individuals were asked to indicate their age with categorical options: age 39 or younger and age 40 or older. Sample data follow.

(a)

Conduct a test of independence to determine whether hours of sleep are independent of age.

State the null and alternative hypotheses.

H₀: Hours of sleep per night is not independent of age.
H_a: Hours of sleep per night is independent of age.H₀: The proportion of people who get 8 or more hours of sleep per night is not equal across the two age groups.
H_a: The proportion of people who get 8 or more hours of sleep per night is equal across the two age groups.    H₀: Hours of sleep per night is independent of age.
H_a: Hours of sleep per night is not independent of age.H₀: Hours of sleep per night is mutually exclusive from age.
H_a: Hours of sleep per night is not mutually exclusive from age.

Find the value of the test statistic. (Round your answer to three decimal places.)

What is the p-value? (Round your answer to four decimal places.)

p-value =

Using a 0.05 level of significance, what is your conclusion?

Do not reject H₀. We cannot conclude that hours of sleep per night and age are not independent.Reject H₀. We cannot conclude that hours of sleep per night and age are independent.    Reject H₀. We conclude that hours of sleep per night and age are not independent.Do not reject H₀. We conclude that hours of sleep per night and age are independent.

(b)

What is your estimate of the percentages of individuals who sleep fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8 hours or more per night?

Fewer than 6 %6 to 6.9 %7 to 7.9 %8 or more %

You may need to use the appropriate technology to answer this question.

A survey was conducted to determine whether hours of sleep per night are independent of age. A sample of individuals was asked to indicate the number of hours of sleep per night with categorical options: fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8 hours or more. Later in the survey, the individuals were asked to indicate their age with categorical options: age 39 or younger and age 40 or older. Sample data follow.

(a)

Conduct a test of independence to determine whether hours of sleep are independent of age.

State the null and alternative hypotheses.

H₀: Hours of sleep per night is not independent of age.
H_a: Hours of sleep per night is independent of age.H₀: The proportion of people who get 8 or more hours of sleep per night is not equal across the two age groups.
H_a: The proportion of people who get 8 or more hours of sleep per night is equal across the two age groups.    H₀: Hours of sleep per night is mutually exclusive from age.
H_a: Hours of sleep per night is not mutually exclusive from age.H₀: Hours of sleep per night is independent of age.
H_a: Hours of sleep per night is not independent of age.

Find the value of the test statistic. (Round your answer to three decimal places.)

What is the p-value? (Round your answer to four decimal places.)

p-value =

Using a 0.05 level of significance, what is your conclusion?

Reject H₀. We cannot conclude that hours of sleep per night and age are independent.Reject H₀. We conclude that hours of sleep per night and age are not independent.    Do not reject H₀. We cannot conclude that hours of sleep per night and age are not independent.Do not reject H₀. We conclude that hours of sleep per night and age are independent.

(b)

What is your estimate of the percentages of individuals who sleep fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8 hours or more per night?

Fewer than 6 % =

6 to 6.9 % =

7 to 7.9 %=

8 or more % =

Analyze the following sentences and rewrite them in a more concise manner (using active voice where applicable), cutting out as many unnecessary words and phrases as possible without reducing the meaning of each passage.
1. It is thought by Trudy that her young puppy dog, which constantly runs, jumps, scampers, and rushes around the house, is in need of more walks over the course of an entire day.
2. At this point in time, the actions of Richard towards his colleagues and co-workers will be
considered unacceptable and unsatisfactory by the department supervisors.

Find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1. z= -0.95 A symmetric bell-shaped curve is plotted over a horizontal scale. A vertical line runs from the scale to the curve at labeled coordinate “z equals negative 0.95,” which is to the left of the curve’s center and peak. The area under the curve to the right of the vertical line is shaded. The area of the shaded region is nothing. ?(Round to four decimal places as? needed.)

Suppose an object that has a mass of 8.8 kg and slides on ice at a speed of 13 m/s. It runs into another object, which is initially at rest and has a mass of 11.10 kg. They naturally stick together (in a perfectly elastic colision). What is their final velocity in (m/s)?

A 160 kg merry-go-round has a radius of 2.5 m and it is rotating with an angular velocity of 0.7 rev/s. What is its angular velocity after an at rest 86-kg person gets onto it by grabbing its outer edge?