The Cheebles cookie factory changed their recipe. The inspectors took a sample of the new cookies and found that the sample was 42 grams with a standard deviation of 4 grams. the Cheebles CEO specially asked the inspectors to use these statistics to find the lower and upper boundary weighs of 50% of their cookies. What are the Z values of the limits of the limits of the area covering the middle half of the area under the normal curve that the inspectors would use to find this information for the CEO of Cheebles?

In the city of Urbanville, land is divided between supermarkets and houses (for residents). There is a train station at x = 0.

- Urbanville residents all work from home. Their utility of living in the city is U = 20 − R, where R is the rent they pay. These residents also have the option of moving out of the city and living far away from Urbanville. Doing so gives them a utility of U₀ = 18.

- Supermarkets receive goods from the central train station. Their profits are π = P_g − 2d − R. In the profit equation, d stands for the distance to the train station.

- The price of groceries is P_g= 10.

(a) Draw the bid rent curves for supermarkets and houses (b_s and b_h).

(b) Find x* , such that land from 0 to x* is used for supermarkets and land farther away than x* is used for houses.
(c) Draw the new bid-rent curve for supermarkets (b'_s ) and find x₁, the new boundary between supermarkets and houses.

Transportation costs fall, such that supermarket profits are now given by π' = P_g − d − R.

(d) On the same diagram as before, draw the new bid-rent curve for supermarkets (b'_s ) and find x1, the new boundary between supermarkets and houses.

Q2.

(a) What are the differences between an energy based ligand design method such as GRID and a
knowledge based one like LUDI? What are the requirements of a knowledge based ligand design
method?

(b) Interpret the following QSAR equation: log (1/C)=k 1 ?-k 2 ? 2 + k 3 ?. How are factorial design
methods using in QSAR compound selection? Briefly outline how multiple linear regression analysis is
used in the derivation of a QSAR equation. How is cross-validation used for checking the quality of a
regression based QSAR model?

Q3.

(a) Use the example of molecular docking of the antibiotic netropsin to DNA to distinguish
quantitatively the differences between steepest descent and conjugate gradient methods for initial
refinement and stringent minimization. What qualitative conclusions can be drawn about the efficacy
of these two minimization techniques with respect to this docking experiment?

(b) Using two
examples, explain the thermodynamic differences between the Molecular Dynamics and Monte Carlo
methods. What are the advantages to choosing periodic boundary conditions in ANY molecular
simulation of a macromolecule? Use a diagram to plot 4 such periodic cell shapes. What important
class of applied molecular simulations have benefitted from the usage of periodic boundary

Data from 1991 General Social Survey classify a sample of Americans according to their gender and their opinion about afterlife (example from A. Agresti, 1996, “Introduction to categorical data analysis”). The opinions about afterlife were classified into two categories: Yes and No (or undecided). For example, for the females in the sample - 435 said that they believed in an afterlife and 147 said that they did not or were undecided.

Estimate the proportion of females who believed in an afterlife (Use a 95% Confidence Interval).

Test hypothesis that the majority of females (that is, more than 50% females) believed in an afterlife.

- Using a z-score test

Using c² test

The heat evolved in calories per gram of a cement mixture is approximately normally distributed. The population mean is thought to be 100, and the population standard deviation σ is 2. You wish to test H0 : µ = 100 versus H1 : µ 6= 100. Note that this is a two-sided test and they give you σ, the population standard deviation. (a) State the distribution of X¯ assuming that the null is true and n = 9.

(b) Find the boundary of the rejection region for the test statistic (these critical values will be z-values) if the type I error probability is α = 0.01.

(c) Find the boundary of the rejection region in terms of ¯x if the type I error probability is α = 0.01. In other words, how much lower than 100 must X¯ be to reject and how much higher than 100 must X¯ be to reject. You will have an ¯xlow and an ¯xhigh defining the rejection region. HINT: You are un-standardizing your z from part (b) here.

(d) What is the type I error probability α for the test if the acceptance region for the hypothesis test is instead defined as 98.5 ≤ x¯ ≤ 101.5? Recall that α is the probability of rejecting H0 when H0 is actually true.

UK is small open economy with a flexible exchange rate regime and perfect capital mobility. Suppose that the consumption function shifts down, due perhaps to a worsening of consumer confidence. That is, for every level of disposable income, consumers want to consume less. Explain the direction of the effect of this change on output, consumption, investment, interest rate, net exports and exchange rate.

UK is small open economy with a flexible exchange rate regime and perfect capital mobility.
Suppose that the consumption function shifts down, due perhaps to a worsening of consumer confidence. That is, for every level of disposable income, consumers want to consume less. Explain the direction of the effect of this change on output, consumption, investment, interest rate, net exports and exchange rate.

Provide in each case a brief explanation articulating why the statement may be true, false or even uncertain.

Quantitative Easing is likely to be riskier as an antidote for the current crisis for emerging economies such as the Philippines, Indonesia, South Africa, Chile, Brazil, and Turkey than for developed economies such as the U.S., UK, Eurozone, Canada, Australia or New Zealand. (Word limit 300)

Smart-A-Runners Ltd based in Hatfield UK is considering adopting a track and trace system for their supply chain. The company will be using computer simulation to evaluate the benefits of the track and trace system. Briefly discuss how simulation can be used to evaluate the benefits of Smart-A-Runners Ltd’s track and trace system and explain to the company the key issues to consider in their use of simulation.