Suppose that a class contains 15 boys and 30 girls

Suppose that a class contains 15 boys and 30 girls

Week 4 forum

Suppose that a class contains 15 boys and 30 girls, and that 10 students are to be selected at random for a special assignment. Find the probability that exactly 3 boys will be selected.

To make a post to this week’s Challenge Discussion Forum, click on the “Counting isn’t always easy” link, then click Post New Thread. In the title block of the dialog box that appears kindly insert your first and last name; compose your post in the message box; and then click Post Message.

 

Week 6 forum

Suppose that the percentage annual return you obtain when you invest a dollar in gold or the stock market is dependent on the general state of the national economy as indicated below. For example, the probability that the economy will be in “boom” state is 0.15. In this case, if you invest in the stock market your return is assumed to be 25%; on the other hand if you invest in gold when the economy is in a “boom” state your return will be minus 30%. Likewise for the other possible states of the economy. Note that the sum of the probabilities has to be 1–and is.

State of Economy***Probability***MarketReturn***GoldReturn
Boom****************0.15************25%*************(-30%)
Moderate Growth******0.35************20%***************(-9%)
Weak Growth*********0.25*************5%**************35%
No Growth***********0.25***********(-14%)**************50%

Based on the expected return, would you rather invest your money in the stock market or in gold? Why?

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Week 7 forum

Suppose that the demand for a company’s product in weeks 1, 2, and 3 are each normally distributed and the mean demand during each of these three weeks is 50, 45, and 65, respectively. Suppose the standard deviation of the demand during each of these three weeks is known to be 10, 5, and 15, respectively. It turns out that if we can assume that these three demands are probabilistically independent then the total demand for the three week period is also normally distributed. And, the mean demand for the entire three week period is the sum of the individual means. Likewise, the variance of the demand for the entire three week period is the sum of the individual weekly variances. But be careful! The standard deviation of the demand for the entire 3 week period is not the sum of the individual standard deviations. Square roots don’t work that way!

Now, suppose that the company currently has 180 units in stock, and it will not be receiving any further shipments from its supplier for at least 3 weeks. What is the probability that the company will run out of units?

To make a post to this week’s Challenge Discussion Forum, click on the Using the Normal Distribution link, then click Post New Thread. In the title block of the dialog box that appears kindly insert your first and last name; compose your post in the message box; and then click Post Message.

Week 10 forum

Political polls typically sample randomly from the U.S population to investigate the percentage of voters who favor some candidate or issue. The number of people polled is usually on the order of 1000. Suppose that one such poll asks voters how they feel about the President’s handling of the crisis in the financial markets. The results show that 575 out of the 1280 people polled say they either “approve” or “strongly approve” of the President’s handling of this matter. Based on the sample referenced above, find a 95% confidence interval estimate for the proportion of the entire voter population who “approve” or “strongly approve” of the President’s handling of the crisis in the financial markets.

Now, here’s an interesting twist. If the same sample proportion was found in a sample twice as large—that is, 1150 out of 2560—how would this affect the confidence interval?

To make a post to this week’s Challenge Discussion Forum, click on the Build a Confidence Interval Estimate link, then click Post New Thread. In the title block of the dialog box that appears kindly insert your first and last name; compose your post in the message box; and then click Post Message.

Week 12 forum

A new process for producing synthetic diamonds can be operated at a profitable level only if the average weight of the diamonds produced by the process is greater than 0.5 karat. To evaluate the profitability of the process, a sample of six diamonds was generated using this new process, with recorded weights .46, .61, .52, .48, .57, and .54 karat. Do the six measurements present sufficient evidence to indicate that the average weight of the diamonds produced by the new process is in excess of 0.5 karat? To answer this question conduct an appropriate test of hypothesis using the five step process outlined in our textbook and utilized in the solutions to the Chapter 8 review problems, which are posted in the Review Problem Sets Solutions folder in the Resources section of our classroom.

To make a post to this week’s Challenge Discussion Forum, click on the Testing a Hypothesis link, then click Post New Thread. In the title block of the dialog box that appears kindly insert your first and last name; compose your post in the message box; and then click Post Message.