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The methodology was otherwise exactly the same as the one we use for our approval ratings tracker , with one minor exception. In our approval-ratings tracker, we run the numbers based on polls that were published as of a given date. For instance, if a poll was conducted from April 16 through April 19, but wasn’t released until April 21, it wouldn’t affect Trump’s approval rating estimate until April 21. For this article, we ran the numbers based on the dates on which the polls had been conducted. A poll that finished its interviewing on April 19 would be reflected beginning in the April 19 estimate, for instance.

Specifically, the estimates start on Jan. 25. Prior to that, the estimates were unstable because few polls had been conducted.

After a slight uptick in the first two to three weeks of his term, Trump’s strong approval ratings have headed downward. But it hasn’t been a steady decline. Instead, they fell considerably from about 29 percent on March 6 — when Republicans How Much Sale Online Suede LaceUp Trainers Sales Up to 50 Tommy Hilfiger Outlet Very Cheap Sale Best Store To Get Extremely vh5DA
— to around 24 percent on April 1, shortly after the GOP pulled the bill from the House floor . They then remained stable for much of April, before beginning to fall again this month after the reintroduction (and House passage) of the health care bill and after Trump fired FBI director James Comey on May 9. As of Tuesday, just 21.4 percent of Americans strongly approved of Trump’s performance.

By comparison, 45 percent of Americans strongly approved of President Obama’s performance as of April 2009, although Obama’s strong approval numbers would Quality From China Cheap Free Shipping From China Velvet Pumps Magenta Marni Best Choice For Sale Cheap Real LPg6qD9CPt
— to the mid-to-high 20s by the midterms and to the high teens by 2014.

The share of Americans who somewhat approve of Trump’s performance has actually increased slightly, however, from about 16 percent in early February to 17.9 percent as of Tuesday. In part, this probably reflects voters who once strongly approved of Trump and who have now downgraded him to the somewhat approve category. (Trump’s strongly approve and somewhat approve numbers have been inversely correlated so far, meaning that as one has risen, the other has tended to fall.) A potential problem for Trump is that in the event of continued White House turmoil, the next step for these somewhat approve voters would be to move toward disapproval of the president.

The number of Americans who strongly disapprove of Trump has sharply risen since early in his term, meanwhile, from the mid-30s in early February to 44.1 percent as of Tuesday. In most surveys, Trump’s strongly disapprove rating exceeds his overall approval rating, in fact.

The bulk of the increase in Trump’s strong disapproval ratings came early in his term, over the course of late January and early February. It’s possible that this was partly a reaction to Trump’s initial Womens Carlita Metal Canvas/Flocking Trainers Calvin Klein High Quality Cheap Price New Arrival Where To Buy vUIIh
on immigrants from seven predominantly Muslim countries, which was the biggest news of Trump’s first few weeks in office. But presidential disapproval often rises in the first month or so of a president’s tenure as voters who initially give a new president the benefit of the doubt find things to dislike in his performance.

An Application: Consider two investment alternatives, Investment I and Investment II with the characteristics outlined in the following table:

To rank these two investments under the Standard Dominance Approach in Finance , first we must compute the mean and standard deviation and then analyze the results. Using the Multinomial for calculation, we notice that the Investment I has mean = 6.75% and standard deviation = 3.9%, while the second investment has mean = 5.36% and standard deviation = 2.06%. First observe that under the usual mean-variance analysis, these two investments cannot be ranked. This is because the first investment has the greater mean; it also has the greater standard deviation; therefore, the Standard Dominance Approach is not a useful tool here. We have to resort to the coefficient of variation (C.V.) as a systematic basis of comparison. The C.V. for Investment I is 57.74% and for Investment II is 38.43%. Therefore, Investment II has preference over the Investment I. Clearly, this approach can be used to rank any number of alternative investments. Notice that less variation in return on investment implies less risk.

Expectation of a sum of a random number of random variables: Suppose that the number of people entering a department store on a given day is a random variable with mean 50. Suppose further that the amount of money spent by these customers is independent random variables having a common mean of $80. What is the expected amount of money spent in the store on a given day?.

Hence, the expected amount of money spent in the store is (50)(80) = $4000.

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in performing some numerical experimentation to:

Many applications arise from the central limit theorem (CLT). The CLT states that, average of values of n observations approaches normal distribution, irrespective of the form of original distribution under quite general conditions. Consequently, normal distribution is an appropriate model for many, but not all, physical phenomena, such as distribution of physical measurements on living organisms, intelligence test scores, product dimensions, average temperatures, and so on.

Know that the Normal distribution is to satisfy seven requirements: (1) the graph should be bell shaped curve; (2) mean, median and mode are all equal; (3) mean, median and mode are located at the center of the distribution; (4) it has only one mode, (5) it is symmetric about mean, (6) it is a continuous function; (6) it never touches x-axis; and (7) the area under curve equals one.

Many methods of statistical analysis presume normal distribution.

When we know the mean and variance of a Normal then it allows us to find probabilities. So, if, for example, you knew some things about the average height of women in the nation, including the fact that heights are distributed normally, you could measure all the women in your extended family and find the average height. This enables you to determine a probability associated with your result, if the probability of getting your result, given your knowledge of women nationwide, is high. Then your family's female height cannot be said to be different from average. If that probability is low, then your result is rare (given the knowledge about women nationwide), and you can say your family is different. You have just completed a test of the hypothesis that the average height of women in your family is different from the overall average.