if you randomly answer a t/f test and want to figure the possibililty of gettng at least an 80......how do you start and then once you have done this, what if you want to try it 4 more times? HELP
Let N be the number of questions. You are asking for the probability of getting N/5 or fewer wrong by randomly guessing.
Assume N>> 1 and use an error-function approximation for the number of questions answered correctly. The mean will be N/2 and the standard deviation will be sqrt[N*p*(1-p)] = (1/2)sqrtN, since p = 1/2 is the probability of getting each one right.
Inegrate the probability of correct answers from 0.8 N to N, which you can treat as infinity when N is very large.
The larger the value of N, the less likely you will be to get 80% right.
For N=25, I get a standard deviation of 2.5 about a mean of 12.5, and the probability of getting 20 or more right will be 0.0013. It becomes a much lower probability of N = 100. You need to use an error function table for this sort of problem.
To calculate the probability of getting at least 80% correct on a True/False test, you can use the binomial distribution. The probability of getting a question correct is 1/2 (assuming an equal chance of selecting True or False). Let's say you have N questions on the test.
To start, calculate the probability of getting exactly 80% correct:
P(X = 0.8N) = (N choose 0.8N) * (1/2)^(0.8N) * (1/2)^(0.2N)
To calculate the probability of getting at least 80% correct, you need to sum up the probabilities of getting exactly 80%, 81%, 82%, and so on, up to N correct answers.
P(X >= 0.8N) = P(X = 0.8N) + P(X = 0.8N + 1) + P(X = 0.8N + 2) + ... + P(X = N)
To calculate this, you will need to use a calculator or a statistical software package that can perform binomial calculations.
If you want to repeat this process four more times, simply repeat the calculations for each set of questions, using the same formula. Keep in mind that the probabilities may vary depending on the number of questions and the desired percentage of correct answers.
Alternatively, you can use a binomial calculator or a spreadsheet program that has built-in functions for calculating binomial probabilities. Simply enter the number of questions and the desired percentage, and the software will provide you with the probability of achieving that percentage or higher.
Remember that these calculations assume random guessing and an equal chance of selecting True or False for each question. The actual probability may differ if the questions are not independent or if you have any prior knowledge that might influence your guesses.
To start, calculate the mean and standard deviation for the number of correctly answered questions. In this case, since it's a True/False test and you're randomly guessing, each question has a 50% chance of being answered correctly. Let's assume you have N questions, so the mean would be N/2.
The standard deviation can be calculated using the formula sqrt(N * p * (1-p)), where p is the probability of getting each question right (which is 1/2 in this case). So, the standard deviation is (1/2)sqrt(N).
Now, you want to find the probability of getting at least 80% of the questions right. Since it's a True/False test, that would be equivalent to answering 80% or more questions correctly.
To find this probability, you can use the error function approximation. You'll integrate the probability of getting the correct number of answers from 0.8N to N. When N is very large, you can treat N as infinity in the integration.
The larger the value of N, the less likely it is to get 80% right. For example, for N=25, the standard deviation is 2.5 about a mean of 12.5, and the probability of getting 20 or more right would be 0.0013. This probability becomes even lower for larger values of N, like N=100.
If you want to try this calculation 4 more times, you can use the same steps outlined above for each trial. Just substitute the new value of N each time and repeat the calculations. Remember, as N increases, the probability of getting at least 80% right decreases.