19.The retail price of 1 pound roast ground coffee has a skewed distribution with a mean 4.78 dollars and a standard deviation of 0.61 dollars. A sample random sample of 36 bags of 1 pound roast ground coffee is chosen. Let represent the mean retail price of 36 bags of 1 pound roast ground coffee. (1)(2.5 points) We know the sampling distribution of the sample mean has approximately a normal distribution because of (a)the Law of Large Numbers. (b)the Central Limit Theorem. (c)the population we’re sampling from has a Normal distribution. (d)the Empirical Rule (2)(1.5 points) Compute the mean and standard deviation of the sampling distribution of . (3)(2.5 points) Compute and interpret the z-score for = 4.90. (4)(2.5 points) Compute (5)(3.5 points) Is it unusual that ? Explain why or why not. (you need show your work)

4. Use a model of internal economies of scale, but now allow for firms to have different marginal costs (c ).

a) Explain why opening up to trade results in the lowest cost firms expanding and the highest cost firms shutting down. Draw one or more diagrams to help you explain your points. Is this consistent with empirical evidence on how firms react to trade openness? Assume that there are no trade costs for part a.

b) Now assume that some trade cost (t) exists in order for a firm to export, per unit. How will increasing the trade cost t affect which types of firms export and which do not? From your answer, how would you conclude Canadian firms and consumers might be affected by a potential collapse of the North American Free Trade Agreement (NAFTA)? You may want to draw a diagram to help make your points in the first part of the question, although it is not absolutely necessary.

Enzyme X is a highly pigmented protein that imparts the characteristic color to certain blue-green algae. It also facilitates a reaction necessary to the survival of this species; we can follow the kinetics of this reaction by measuring the conversion of Substance X to Substance Y at various times during purification.

Given a pure preparation of these algae, and the required supplies and equipment, devise and outline an empirical procedure for purifying Enzyme X.

What is a good indication of purity in your preparation?

The outline of steps to purify Enzyme X should include detail of what the technique is, why that technique is needed, and what the result will be. The reader needs to have enough information so as to be able to do the experiment. Treat the assignment as one that demonstrates your knowledge of biochemical techniques in protein purification.

As for the length of this assignment, you are describing a protocol; therefore, you need to provide the necessary information for the reader to be able to know how, why, and what, as well as the potential outcomes of the steps and the end result.

Table # 1 presents the probabilistic distribution of the clients that enter Wendy’s in a period of 15 minutes.

Find the expected value and standard deviation of this probability distribution. Find the 68% intervals. 95% and 99% (empirical rule). (Use Excel to answer this question). At the end you must explain in your words what these results mean

If it were a Poisson distribution, find:
What is the probability that exactly 16 customers will enter the fast food restaurant in the next 15 minutes?
What is the probability that 10 or fewer clients will enter in the next 15 minutes?
What is the probability that they enter between 5 <= x <= 15?

1. Length (in days) of human pregnancies is a normal random variable (X) with mean 266, standard deviation 16.

a. The probability is 95% that a pregnancy will last between what 2 days? (Remember your empirical rule here)

b. What is the probability of a pregnancy lasting longer than 315 days?

2. What is the probability that a normal random variable will take a value that is less than 1.05 standard deviations above its mean? In other words, what is P(Z < 1.05)?

3. What is the probability that a normal random variable will take a value that is between 1.5 standard deviations below the mean and 2.5 standard deviations above the mean? In other words, what is P(−1.5 < Z < 2.5)?

4. What is the probability that a normal random variable will take a value that is more than 2.55 standard deviations above its mean? In other words, what is P(Z > 2.55)?

Calculate the exact masses and relative isotopic abundances of all the isotopomers of dichloromethane. Consider only the two most abundant isotopes of carbon and chlorine, and ignore deuterium and tritium (i.e., assume the natural abundance of 1H is 1.000000). Summarize your results by giving in a table the empirical formula for each isotopomer with superscripted atomic masses, the nominal m/z and the exact m/z values for each in a table .

To calculate natural abundance, make a product of the natural abundance of each element raised to the power of the number of times it occurs in the molecule. Then multiply it by the number of distinguishable ways that you can make this isotopomer, if the nuclei are labelled. For example, for two C nuclei labelled A and B, there is only one way to make 13C-13C (13CA13CB) but there are two ways to make 12C-13C (i.e., 13CA12CB and 12CA13CB). When you’re done correctly, all the abundances should add up to 100%, so you can use this to check for errors.

Please do this task by R.

a) Revise the simulation shown in the lecture with the aim of constructing the empirical sampling distribution of beta_hat, based on 5000 trials.

b) According to the lecture, the mean of that histogram is supposed to be approximately equal to the true slope. Is it? Show code.

c) According to the lecture, the standard deviation of that histogram is supposed to be approximately equal to sigma_eps/sqrt(Sxx). Is it? Show code.

d) According to the lecture, the distribution of the beta_hat is supposed to be normal with certain parameters. Use qqnorm() and abline() to confirm that it is normal.

not sure if this help or not,

n = 10

n.trial = 64

x = c(1:n)

y_true = 10 + 2*x

sigma_eps = 15

par(mfrow=c(8,8),mar=c(0,0,0,0))

set.seed(123)

for(trial in 1:n.trial){

y_obs = y_true + rnorm(n,0,sigma_eps)

lm.1 = lm(y_obs ~ x)

plot(x, y_obs)

abline(10,2, col=2)

abline(lm.1, col=4)

}

Match the described probability with the type of probability.

use R

# Problem 4 (5 pts each):
# Set x as a vector of 500 random numbers from Unif(100,300).
# This vector will be kept fixed for the rest of this problem.
#
# (a) Define a function b1(x, beta0, beta1, sigm) that uses the lm() function to
# return the regression line slope b1 for y as a linear function of x, where
#
# y = beta0 + beta1 x + err
#
# and the error term 'err' has a normal N(0,sigm^2) distribution
# (note that standard deviation is equal 'sigm').
#
# Hint: See how the slope b1 is extracted in the initial example of Session 11.

# (b) Replicate the function b1 twenty thousand times for
# beta0 = 15, beta1 = 2, and sigm =10, and store into a vector 'Slopes'.

# (c) Plot the empirical density of Slopes.

# (d) Calculate sample mean and sample variance of Slopes.

# (e) Add to the plot the pdf of a Normal distribution with parameters from part (d).

1. Sorting algorithm for arrays: understand how to perform the following algorithms. (a). Simple sorting

   1. Bubblesort:T(n)ÎO(n2)

   2. Selection sort : T(n) Î O(n2)

   3. Insertion sort: T(n) Î O(n2)

   (b).Advanced sorting

i. Shell sort: O(n2) < O(n1.25) < O(nlogn), O(n1.25) is empirical result for shell sort.

2. Merge sort: T(n) Î O(nlogn), need one temporary array with the same length as the array needed to be sorted.

3. Quick sort: -average case: T(n) Î O(nlogn),
   -worst case(rare occurrence): T(n) Î O(n2)

5. Searching algorithm for arrays: understand how to perform the following algorithms. (a). Searching in unsorted arrays

i. Sequentialsearch
ii. Sequential search with sentinel

(b).Searching in sorted arrays

1. Binary search

2. Interpolation search