Finding Binomial Probabilities Using the TI-84

This paragraph introduces the process of calculating binomial probabilities using a TI-84 calculator, highlighting the importance of formatting and the distinction between two functions: binomial PDF (for specific outcomes) and binomial CDF (for ranges of outcomes). The speaker emphasizes the correct input sequence for each function, which involves entering the total number of trials, the probability of success, and the value or range being sought. An example is given to illustrate the calculation of the probability that exactly ten out of thirteen randomly selected college students drink alcohol, using the binomial PDF function with the values 13 trials, 70% probability of success, and success value of 10, resulting in a probability of approximately 0.218. The speaker also demonstrates how to modify inputs for different scenarios, such as calculating the probability for exactly 13 successes, which yields a result of approximately 0.069.

The second paragraph delves into calculating the probability of 'at least' a certain number of successes in a binomial distribution. The speaker explains how to break down the problem into separate probabilities for exact values and then sum them up. An example is provided where the probability of at least eleven out of thirteen college students drinking alcohol is calculated by adding the probabilities for exactly eleven, twelve, and thirteen successes, using the binomial PDF function. The speaker also contrasts this method with using the binomial CDF function, which simplifies the process by calculating the range directly. The paragraph also discusses the importance of correctly using the binomial PDF function to avoid errors and the utility of the CDF function in handling ranges, as demonstrated with the probability of fewer than four students drinking alcohol, rewritten as 'less than or equal to three' to fit the CDF function requirements.

In this paragraph, the speaker discusses the use of the complement rule and the binomial CDF function to calculate probabilities for ranges, specifically 'at least' and 'at most' scenarios. The speaker shows how to rewrite a probability statement to fit the calculator's requirements and demonstrates the calculation of the probability that at least four out of thirteen students drink alcohol using the complement rule, which involves subtracting the probability of the complementary event (less than or equal to three students) from one. The speaker also explains how to calculate the probability of at most four students drinking alcohol directly using the binomial CDF function and contrasts it with the probability of more than four students, which is also found using the complement rule. The importance of using the correct function and input format is reiterated, with examples showing how to convert probabilities from scientific notation for ease of interpretation.

The final paragraph summarizes the key differences between using the binomial PDF and CDF functions on the TI-84 calculator. The speaker clarifies that the PDF function is used for calculating exact values without a range, while the CDF function is used for finding probabilities within a range. It is emphasized that the third input in the CDF function should be the highest possible value within the range of interest. The speaker also advises on how to handle open intervals by converting them into a format that the calculator can process, such as changing 'less than' to 'less than or equal to' and adjusting the input values accordingly. This paragraph reinforces the importance of understanding the functions and input requirements to accurately calculate binomial probabilities.