There are five parts to this discussion, and you must complete all 5 in order to earn full credit. By now, everyone should be familiar with how to calculate a sample data of 30 from the population data set. The True Average and Population SD rom the original data set of 1164 observations for Average Wage is $48,011 and $17,329 respectively. You need to calculate the Average and the Sample SD from your sample of 30 for the variable ″Average Wage″. Part 1) Find the probability that your Average Salary for your sample is less than the True Average Salary from the population and interpret your results. Round to 4 decimal places and then convert those 4 decimal places in to percents to interpret your probability. Here is some code that will help you with Part 1) but you need to figure out Part 2) and Part 3) on your own. prob ˂- pnorm(x, 48011, sd) round(prob, 4) Part 2) You are told that once you graduate with your Bachelor′s degree you will get a $5,000 bonus. Adding that $5,000 to your sample average, what is the probability that an individual′s salary exceeds $5,000 plus the sample average, given that it exceeds the population average? Interpret your results. Round to 4 decimal places and then convert those 4 decimal places in to percents to interpret your probability. Part 3) What is the probability that after you graduate with your Bachelor′s degree your Salary will be less than $51,000, given that it is larger than $45,000. Interpret your results. Round to 4 decimal places and then convert those 4 decimal places in to percents to interpret your probability. Hint: You will use the pnorm function in R twice. Part 4) Using your sample average and sample SD from your sample size of 30. We want to divide the Salary into the Lower 25%, Middle 50%, Upper 25%, and then the Upper 10% and Upper 5%. Interpret these 5 values. Once you calculate these 5 values, find the proportions of men and women in each range. Find the proportion of Degree Type in each range? From the proportion of Occupation in each range? Do these proportions surprise you? What is something interesting you noticed? Summarize your results and write up a summary of your results. Here is some code to help you with the Lower 25%, but you need to figure out the other 4 values on your own. qnorm(0.25, sample average, sample SD) Part 5a) (Mandatory) The probability density function (pdf) is obtained in R with pnorm. To plot a normal curve, use the function curve with dnorm as the argument. Plot the normal curve using your sample mean and SD. curve (dnorm(x, mean, sd), from ＝ mean-4*sd, to ＝ mean+4*sd, ylab ＝ ″f(x)″, xlab＝″Salary″) For Part 5b) (Not Mandatory) All you have to do is plot the probability density function for the Average Wage. If you want to plot the function for Males and Females in the same graph you can do this for extra credit. In Chapter 18, Fig. 18.2 shows you how to plot both males and females. This is not mandatory for it can be done for extra credit and extra practice. plot(NA, xlab ＝ ″Height(m)″, xlim ＝ c(0.5, 3), ylab ＝ ″f(x)″, ylim ＝ c(0, 1.6)) # the x, y axes curve(dnorm(x, 1.65, 0.25), add ＝ TRUE) curve(dnorm(x, 1.85, 0.25), add ＝ TRUE) text(1.15, 0.5, ″Females″) text(2.35, 0.5, ″Males″) Write up a summary of your results. Instructions: Your initial post should be at least 150 words. You must also respond to at least 2 other students outside your initial thread. Responses should be a minimum of 100 words and may include direct questions. Ideas for peer posts: comment on their probabilities, you can compare your values to the random sample they go and see how different the numbers are. What surprised you? What didn′t surprise you? How can you use probability in your day to day life to help make better and more informed decisions?
