Assume that the population of a town obeys Malthusian growth. Assume that the size of the population was 2000 in year 1900, and 50 000 in year 1950.

(a) Find the value of the growth constant k.
(b) How long does it take for the population to grow by 20%?
(c) How big was the population in year 2000?
(d) What was the rate of change of the population in year 2000?
(e) Calculate the size of the population in year 2001, and from that the actual change in population during the one year, from 2000 to 2001.
(f) Explain why the two values calculated in (d) and (e) above do not necessarily have to be the same.

A particular intersection in a small town is equipped with a surveillance camera. The number of traffic tickets issued to drivers passing through the intersection follows the Poisson distribution and averages 4.5 per month.

a. What is the probability that 5 traffic tickets will be issued at the intersection next​ month?

b. What is the probability that 3 or fewer traffic tickets will be issued at the intersection next​ month?

c. What is the probability that more than 6 traffic tickets will be issued at the intersection next​ month?

There is a town with 100 identical residents with initial wealth of $1000 and a utility function u = √ (wealth). Every person owns a car and there is a probability p = .2 that a person’s car will need a costly repair in a given year. If a person needs a repair, they must pay $500 to fix it.

1. What is the maximum amount that a person would be willing to pay to insure their self against the cost of repairing their car?

2. Suppose a single company exists to offer these insurance policies. What price do they charge? What are their expected profits?

3. What is the probability that the insurance company incurs a loss in a given year?

The number of University graduates in a town is estimated to follow
a Binomial distribution with the probability of success p = 0.6. To
test the null hypothesis a random sample of 15 adults is selected. If
the number of graduates in the sample is between 6 and 12 inclusive,
we shall accept the null hypothesis to be p = 0.6, otherwise we shall
conclude that p 6= 0.6. Use the normal approximation to the binomial
distribution to

(ii) Find the power of the test for p = 0.5

  XSU is a state university located in the town of Xanadu.   Xanadu is located on a large river with many towns within an easy 15-minute drive. Once, the neighborhoods around XSU where all single-family housing but the growth in prestige in XSU caused a large growth in student enrollment over the years, so more and more of the single-family houses were renovated into student housing.    The city did not zone those neighborhoods for exclusive single-family homes. And, the city has no history of enforcing building codes. Now, the city of Xanadu faces problems of access to parking in those neighborhoods, along with dilapidated student housing.   Both students and neighbors are mounting campaigns to address these issues.

      Moreover, XSU has just finished building off-campus student apartments (which are full), and plans upgrading its out-dated dorms with new ones.   Landlords complain about vacancy rates, which currently run about 8%.   Landlords are upset with the bad publicity along with the “unfair” competition from XSU (XSU pays no property taxes).

     City officials have come up with some alternative plans to deal with these issues. One plan is to limit conversions to student rentals to 30% of a block with all current student rental “grandfathered” in. A competing plan is to enforce building codes with vigorous semi-annual inspections of all rental properties, complete with hefty fines and condemnations.

Using demand and supply curves, show and explain the likely effects of successively implementing the 30% conversion restriction.

on the rental price of housing and the quantity of rental housing in Xanadu.

b. on the rental price of housing and the quantity of rental housing in neighboring towns.

2. Show and explain the likely effects of successively implementing the semi-annual inspections of all rental housing

a. on the rental price of housing and the quantity of rental housing in Xanadu

b. on the rental price of housing and the quantity of rental housing in neighboring towns.

3. Explain which proposal you would expect landlords to endorse.

4. Explain which proposal you would expect XSU students to endorse.

The mayor of a town has proposed a plan for the construction of an adjoining community. A political study took a sample of 1200 voters in the town and found that 45% of the residents favored construction. Using the data, a political strategist wants to test the claim that the percentage of residents who favor construction is not equal 48%. Testing at the 0.01 level, is there enough evidence to support the strategist's claim?

Step 1 of 7 : State the null and alternative hypotheses.

Step 2 of 7: Find the value of the test statistic. Round your answer to two decimal places.

Step 3 of 7: Specify if the test is one-tailed or two-tailed.

Step 4 of 7: Determine the P-value of the test statistic. Round your answer to four decimal places.

Step 5 of 7: Identify the value of the level of significance.

Step 6 of 7: Make the decision to reject or fail to reject the null hypothesis.

Step 7 of 7: State the conclusion of the hypothesis test.

1. The mayor of a town believes that 78% of the residents favor annexation of an adjoining community. Is there sufficient evidence at the 0.01 level to dispute the mayor's claim?

State the null and alternative hypotheses for the above scenario

2.The mayor of a town believes that more than 72% of the residents favor construction of an adjoining community. Is there sufficient evidence at the 0.05 level to support the mayor's claim?

3. A newsletter publisher believes that over 71% of their readers own a Rolls Royce. For marketing purposes, a potential advertiser wants to confirm this claim. After performing a test at the 0.02 level of significance, the advertiser decides to reject the null hypothesis.

What is the conclusion regarding the publisher's claim?

a. There is sufficient evidence at the 0.02 level of significance that the percentage is over 71%.

b.There is not sufficient evidence at the 0.02 level of significance to say that the percentage is over 71%

4.A publisher reports that 53% of their readers own a personal computer. A marketing executive wants to test the claim that the percentage is actually over the reported percentage. A random sample of 310 found that 57% of the readers owned a personal computer. Is there sufficient evidence at the 0.01 level to support the executive's claim?

-State the null and alternative hypotheses.

-Find the value of the test statistic. Round your answer to two decimal places.

-Specify if the test is one-tailed or two-tailed.

-Determine the decision rule for rejecting the null hypothesis, H0.

-Make the decision to reject or fail to reject the null hypothesis.

Matthew owns a piece of land with a toy factory on it in a small town near Melbourne city. The factory is a family business that started a century ago and is currently used to produce handmade wooden toys. However, for market participants, they would redevelop the land to build a retail shopping centre. Matthew recently received an attractive offer from property redevelopers, but he rejected the offer because he has no intention to stop the family business.

Which of the following statements is correct regarding the fair value of land?

Group of answer choices

The fair value of the land cannot be determined because we do not know the highest and best use of the asset.

The fair value of the land should be based on its current use as Matthew has no intention to sell the land and stop the family business.

The fair value of the land should be based on stand-alone valuation premise.

The fair value of the land should be based on in-combination valuation premise.

In a town, 36% of the citizens contributed to the Republicans, 46% contributed to the Democrats, and 12% contributed to both. What percentage contributed to neither party?

A box contains 4 white, 3 red, and 3 black marbles. One marble is chosen at random, and it is not black. Find the probability that it is white. (Enter your answer as a fraction.)

Suppose that 90% of drivers are "careful" and 10% are "reckless." Suppose further that a careful driver has a 0.2 probability of being in an accident in a given year, while for a reckless driver the probability is 0.3. What is the probability that a randomly selected driver will have an accident within a year? (Enter your answer to two decimal places.)

To provide a service to a town, water is taken from a dam and raised to a tank from where it is distributed to the neighborhood. The difference in levels between the dam and the tank is 600 feet; the length of the commercial steel pipe is 40,000 feet and the required flow is 8,000 gpm. Define:
a) the necessary pumping station
b) The type of pumps
c) The turning speed
d) Diameter of impellers
e) Power necessary to provide this service.