he weight of an organ in adult males has a​ bell-shaped distribution with a mean of 320 grams and a standard deviation of 45 grams. Use the empirical rule to determine the following. ​

(a) About 99.7​% of organs will be between what​ weights?

​(b) What percentage of organs weighs between 230 grams and 410 ​grams? ​

(c) What percentage of organs weighs less than 230 grams or more than 410 ​grams? ​

(d) What percentage of organs weighs between 275 grams and 455 ​grams?

Implement heap sort by using the bottom-up insertion 
method. Add this sort to your sorting framework. Evaluate
its performance in terms of the numbers of comparisons and
exchanges, and compare it to the performance of the two
advanced sorting methods that you have previously implemented.
Submit your report with detailed empirical results and a
thorough explanation of these results. Which of the three
advanced sorting method is the best choice for a) ordered
data, b) data in reverse order, and c) average data for the data sets
you have experimented with.

(Java)

The following data is given for a horizontal highway curve having 2 lanes with Lane width of 3.65 m each: Ruling design speed is 110kmph, Allowable rate of change of circular acceleration = 0.5 to 0.8. Allowable rate of introduction of super-elevation = 1 in 144, Take maximum allowable superelevation and lateral frictional co-efficient is 0.15.

Calculate the length of a transition curve for following cases.

Rate of change of centrifugal acceleration (C).

Rate of introduction of super-elevation.

Using empirical equations for plain and mountainous terrain.

1. This question concerns our short run model of exchange rate determination.

1. Why do we need a different model of exchange rates in the short run and the long run? Your answer should include some reference to empirical evidence.

2. Assume we are in the short run, and assume that the Federal Reserve keeps the supply of dollars fixed. The U.S. has an excellent corn harvest this year, so real output Y goes up. Explain what you expect to happen to the dollar-euro exchange rate E$/€ and why.

Each of the distributions below could be used to model the time spent studying for an exam. Take one random sample of size 25 from each of the distributions below. Then, take 1,000 resamples (i.e., sample with replacement) of size 25 from your sample. In each case (a,b,c), plot the empirical distribution of the sample mean, estimate the mean of the sample mean, and estimate the standard deviation of the sample mean. Compare the results to the theoretical results.

a. N(5, 1.52)

b. Unif(0,10)

c. Gamma(5,1)

Using Rstudio

# 1. Monty-Hall Three doors

Recall the Monty-Hall game with three doors, discussed in class. Run a simulation to check that the probablility of winning increases to 2/3 if we switch doors at step two.

Set up the experiment two functions "monty_3doors_noswitch" and "monty_3doors_switch" (these functions will have no input values):

```{r}
monty_3doors_noswitch <- function(){
  
}

monty_3doors_switch <- function(){
  
}

```

Use your two functions and the replicate function to compute the empirical probablility of winning for the two experiments.
Compare your answers with the actual theoretical predictions.

```{r}

```

Part 1: Random Data, Statistics, and the Empirical Rule **Data Set Below**

Methods: Use Excel (or similar software) to create the tables and graph. Then copy the items and paste them into a Word document. The tables should be formatted vertically, have borders, and be given the labels and titles stated in the assignment. The proper symbols should be used. Do not submit this assignment as an Excel file. The completed assignment should be a Word (or .pdf) document.

1. The data values and relevant information are posted in the course website. Use the data set (P, Q, R, S, or T) assigned to you by your instructor to complete this application.

For the purpose of this application, treat the data set as if it represented a certain random variable and was a valid random sample gathered by a researcher from a normally distributed population. The sample data was actually found with an online Gaussian random number generator that creates normally distributed data values. The random number generator simulates the results of a researcher finding those values through observation or experimentation.

2. Use technology (Excel, graphing calculator, etc.) to sort the sample data values from low to high. Use Excel or similar software to put the data into a table with about 5 or 6 columns. Label this “Table 1: Sorted Set of Sample Data.”

3. Using 5 to 10 class intervals, organize the sample data as a frequency distribution in a table. The intervals of the frequency distribution should be rounded to the tenths so that they match the data. Label this “Table 2: Frequency Distribution.”

4. Use Excel (or similar software) to construct a frequency histogram to illustrate the data. Give the axes the proper titles. Label this “Graph 1: Histogram.”

5. Use Table 2, the frequency distribution, to find the midpoints of each class interval. Create a new frequency distribution with the midpoints in the left column and the frequencies in the right column. Label this “Table 3: Frequency Distribution with Midpoints.”

6. Use technology to find the mean, median, standard deviation, and variance of the sample data organized in Table 3 (from step 5 above). Put these values into a table with the proper symbol in the left column and the value of the statistic in the right column. Also, from the original data set, put the values of the range and sample size in the table. The median and range do not generally have symbols so the terms “Median” and “Range” can be used in the left column. Identify the modal class (the one with the highest frequency). Put the terms “Modal Class” in the left column and the class interval in the right column. The statistics should be rounded properly (one more decimal place than the data). Label this “Table 4: Summary Statistics”
7. Use the sample mean and standard deviation to find the values related to the Empirical Rule.

         The Empirical Rule: For a set of data whose distribution is approximately normal,

• about 68% of the data are within one standard deviation of the mean.
• about 95% of the data are within two standard deviations of the mean.
• about 99.7% of the data are within three standard deviations of the mean.

Use the value of n and the percents listed above to find how many data values should be within each category. Then use the sample mean and standard deviation to find the lower and upper cut-off values in each category. Then use the sorted list of data to determine how many values are actually in each category. Put the values into a table as shown in the example and label it “Table 5: The Empirical Rule.”

There is some evidence that, in the years 1981 - 85, a simple name change resulted in a short-term increase in the price of certain business firms' stocks (relative to the prices of similar stocks). (See D. Horsky and P. Swyngedouw, "Does it pay to change your company's name? A stock market perspective," Marketing Science v.6, pp. 320- 35, 1987.)

Suppose that, to test the profitability of name changes in the more recent market (the past five years), we analyze the stock prices of a large sample of corporations shortly after they changed names, and we find that the mean relative increase in stock price was about 0.72%, with a standard deviation of 0.14%. Suppose that this mean and standard deviation apply to the population of all companies that changed names during the past five years. Complete the following statements about the distribution of relative increases in stock price for all companies that changed names during the past five years.

(a) According to Chebyshev's theorem, at least____ of the relative increases in stock price lie between 0.51 % and 0.93 %.

(b) According to Chebyshev's theorem, at least ____ of the relative increases in stock price lie between 0.44 % and 1.00 %.

(c) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately____ of the relative increases in stock price lie between 0.44 % and 1.00 %.

(d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 99.7% of the relative increases in stock price lie between___%
and ____%.

There is some evidence that, in the years 1981-85, a simple name change resulted in a short-term increase in the price of certain business firms' stocks (relative to the prices of similar stocks). (See D. Horsky and P. Swyngedouw, "Does it pay to change your company's name? A stock market perspective," Marketing Science v.6 , pp. 320-35,1987.) Suppose that, to test the profitability of name changes in the more recent market (the past five years), we analyze the stock prices of a large sample of corporations shortly after they changed names, and we find that the mean relative increase in stock price was about 0.70%, with a standard deviation of 0.15%. Suppose that this mean and standard deviation apply to the population of all companies that changed names during the past five years. Complete the following statements about the distribution of relative increases in stock price for all companies that changed names during the past five years.

a) According to Chebyshev's theorem, at least of the relative increases in stock price lie between 0.25 % and 1.15.

(b) According to Chebyshev's theorem, at least of the relative increases in stock price lie between 0.40 % and 1.00.

(c) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately of the relative increases in stock price lie between 0.40 % and 1.00.

(d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 68% of the relative increases in stock price lie between _% and _%. .