The following contingency table shows the number of two-bedroom apartments grouped by monthly rent and location.

Monthly Rent                      York       Lancaster      Dover              Total
$600 to under $700              6              15                     9                      30
$700 to under $800              30                  21                   24                     75
$800 to under $900             15                  18                    12                      45
Total   51                   54                   45                     150

The probability that a randomly selected apartment from this group has a monthly rental from $700 to under $800 or is located in Lancaster is ________.

Daily demand for a product is 100 units, with a standard deviation of 35 units. The review period is 10 days and the lead time is 5 days. At the time of review there are 40 units in stock.

If 95 percent service probability is desired, how many units should be ordered? (Use Excel's NORMSINV() function to find the correct critical value for the given α-level. Do not round intermediate calculations. Round "z" value to 2 decimal places and final answer to the nearest whole number.)

Ordered Quantity- __________

A city is evaluating the benefits to be achieved by changing the level of waste collection service. The change would result in (i) reduced service to the customer, (ii) an increase in the number of houses served daily by each crew, and (iii) a cost savings that would put off a 10% collection rate increase for 1 year. The existing rate for collection service (two containers per house) is $12.5/month. List the important variables for (i), (ii), (iii) separately that must be evaluated when the change is planned. Discuss the probability for successful implementation of the change.

In a nuclear reactor, in the fission process, neutrons are emitted at high energies. Neutrons are to be thermalized, i.e., their kinetic energies have to be significantly reduced, so that you can increase the probability for the new fission processes. You have a choice of a number of materials such as, say, heavy, water, iron and lead. The neutrons experience elastic collisions with the atoms of these materials and lose their energies. Assuming the target atoms are at rest initially, out of the three materials given about which one would you prefer for the efficient thermalization of neutrons? Give reasons and explanation

Daily demand for a product is 90 units, with a standard deviation of 20 units. The review period is 10 days and the lead time is 8 days. At the time of review there are 70 units in stock.

If 99 percent service probability is desired, how many units should be ordered? (Use Excel's NORMSINV() function to find the correct critical value for the given ?-level. Do not round intermediate calculations. Round "z" value to 2 decimal places and final answer to the nearest whole number.)

Hurricanes hit the United States often and hard, causing some loss of life and enormous economic costs. They are ranked in severity by the Saffir-Simpson scale, which ranges from Category 1 to Category 5, with 5 being the worst. In some years, as many as three hurricanes that rate a Category 3 or higher hit the US coastline. In other years, no hurricane of this severity hits the United States. The following table lists the number of ears that had 0, 1, 2, 3 or more hurricanes of at least Category 3 in severity, over the 100 years of the 20th century.

(a). What is the mean number of severe hurricanes to hit the United States per year?

(b). What model would describe the distribution of hurricanes per year, if they were to hit independently of each other and if the probability of a hurricane were the same in every year?

(c). Test the fit of the model from part (b) to the data. Give test statistic, p-value, and conclusion.

Steinberg Corporation and Dietrich Corporation are identical firms except that Dietrich is more levered. Both companies will remain in business for one more year. The companies' economists agree that the probability of the continuation of the current expansion is 80 percent for the next year and the probability of a recession is 20 percent. If the expansion continues, each firm will generate earnings before interest and taxes (EBIT) of $3.9 million. If a recession occurs, each firm will generate earnings before interest and taxes (EBIT) of $1.3 million. Steinberg's debt obligation requires the firm to pay $930,000 at the end of the year. Dietrich's debt obligation requires the firm to pay $1.4 million at the end of the year. Neither firm pays taxes. Assume a discount rate of 12 percent. a-1. What is the value today of Steinberg's debt and equity? (Do not round intermediate calculations and enter your answers in dollars, not millions of dollars, rounded to the nearest whole number, e.g., 1,234,567. a-2. What is the value today of Dietrich's debt and equity? (Do not round intermediate calculations and enter your answers in dollars, not millions of dollars, rounded to the nearest whole number, e.g., 1,234,567.) b. Steinberg’s CEO recently stated that Steinberg’s value should be higher than Dietrich’s because the firm has less debt and therefore less bankruptcy risk. Do you agree or disagree with this statement?

You are holding a party at home, and everyone is about to participate in the following game.

Each person will write their name on a card. All the cards will then be collected and randomly redistributed (one per person). If anyone gets back the card with their own name then all the cards will be collected and randomly distributed again, and this process will be repeated until no-one is holding the card with their own name.

When everyone has a card with someone else’s name on it, you will call out the name on your card. The called person will then call out the name on their card, and so on, until finally your own name is called out.

If anyone’s name does not get called out at some stage during this game, they will have to drink a whole 1 litre bottle of vodka by midnight.

(a) Suppose that there are five people at your party (including yourself).

(i)Find the probability that no one will have to drink 1 litre of vodka by midnight.

(ii)Then find the expected number of people who will have to drink 1 litre of vodka by midnight.

(b) Derive general formulas for the probability and expectation in (a), ones which are correct for any number of people attending your party (i.e. 2, 3, 4, etc.).

(c)Then apply these two formulas to the cases where there are 2, 3, 4, 5, 10 and 100 people at your party, respectively. Present your results in a table.

(very appreciated write in details, thank you very much)