Final answer:
The student is asking how to calculate the value 'a' for which the cumulative probability P(x < a) is achieved, using concepts from binomial probability distributions. The use of a graphing calculator, such as the TI-83 or TI-84 series, and the binomcdf function is explained for obtaining the probability P(x ≤ a).
Step-by-step explanation:
The student's question pertains to finding a particular value 'a' such that a certain cumulative probability statement, P(x < a), is true. This is a concept within the realm of probability distributions, specifically, the binomial distribution. To calculate P(x ≤ a), one can use a graphing calculator, software, or a binomial table. The probability of a success is denoted by 'p', and the number of trials is represented by 'n'. The function binomcdf stands for the binomial cumulative distribution function and is used to compute the probability that a binomial random variable is less than or equal to a certain value.
For example, to calculate P(x ≤ 12), one could use the following instruction on a TI-83, 83+, 84, or 84+ calculator: binomcdf(n, p, 12). If one needs to find P(x ≥ value), this can be computed using 1 - binomcdf(n, p, number), since the built-in function for greater-than probabilities is not directly available.