# Can You Solve These Challenging AP Stats Problems?

• MHB
• cp102
In summary, your friend is likely to roll doubles by at least his third turn in Monopoly because 5 out of 10,000 people in the U.S. have TB and long term studies show that only about 0.1% of people with TB show a false negative.
cp102
Thank you in advance. I need to know how to do these 3 problems by tomorrow in order to pass my AP stats class. Please help!

1.Your friend is playing Monopoly and is in desperate straits. He is cashless and has just landed in jail. He must either roll a double to get out free or pay \$50 after his third attempt of not getting doubles or be kicked out. He is making no money while in jail. What is the likelihood that he will roll doubles by at least his third turn? Explain your conclusion.

2.As a public school teacher I am required to get a tuberculosis (TB) test every 5 years. This is done by inserting some kind of solution under the skin of my forearm. 48 hours later I’m to report to the nurse and have my TB test “read”. This involves seeing whether my forearm looks “normal” or is red and sploggy where they have injected me with that horrid concoction. Well, suppose that the test is 99% effective, that is, 99% of the time if a person that does not have TB, the test correctly shows negative. Looking up online, we learn from CDC that 5 out of every 10,000 people in the U.S have TB. We also earn that long term studies of this test show that only about 0.1% of people with TB show a false negative. So I go back 48 hours after being given the serum under my skin for a TB test. I can see myself that the spot on my arm is red and swollen. What is the probability that I actually have the disease? Support your conclusion.

3.Research suggests that about 24% of thirteen years olds in the US can pick out the state of Colorado on a political lined map of the country. Assume that this is true.

a. What is the probability that exactly 5 out of a sample of 12 thirteen-year-olds will be able to pick out Colorado on a map?
b. What is the probability that you must sample 5 or more thirteen-year-olds to find the first one who can pick out Colorado on a map?

Hi cp102,

Welcome to MHB! :)

We don't do homework for you but we are very happy to help you figure it out yourself through hints and helpful insight. We also ask that you post 1 problem per thread and show us what you have tried.

So which one of these would you like help with first and what have you tried?

Glad you found us!

## 1. What are the three problems in AP Stats that need to be solved?

The three problems in AP Stats that need to be solved are typically related to descriptive statistics, inferential statistics, and probability. These are fundamental concepts in statistics and are often covered in the AP Stats curriculum.

## 2. How can I improve my understanding of descriptive statistics?

To improve your understanding of descriptive statistics, it is important to review key concepts such as measures of central tendency (mean, median, mode), measures of variability (range, standard deviation), and graphical representations (histograms, box plots, etc.). Additionally, practicing with real-world data sets and interpreting results can also help solidify your understanding.

## 3. What is the best approach for solving inferential statistics problems?

The best approach for solving inferential statistics problems is to first identify the type of problem (e.g. hypothesis testing, confidence intervals) and then follow the appropriate steps for that type. This typically involves setting up the null and alternative hypotheses, choosing a significance level, calculating the test statistic, and making a decision based on the p-value or critical value.

## 4. How can I use probability to solve problems in AP Stats?

Probability is an important concept in statistics and is often used to solve problems related to events and outcomes. To use probability in AP Stats, it is important to understand the basic principles such as the addition and multiplication rules, as well as how to calculate probabilities for independent and dependent events.

## 5. What are some resources that can help me with solving problems in AP Stats?

Some resources that can be helpful for solving problems in AP Stats include textbooks, online tutorials and videos, practice problems and exams, and study groups or tutors. It is also important to review class notes and seek help from your teacher or peers if needed.

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