Final answer:
To calculate the probability p(x≥9) for a binomially distributed variable, one must find the cumulative distribution using either the binomial formula, normal approximation, or Poisson distribution (for large n and small p).
Step-by-step explanation:
The student's question pertains to calculating the probability p(x≥9), where x follows a binomial distribution with n trials and a probability p of success on each trial. To find this probability, one would typically use the binomial probability formula or a statistical table. However, if the approximate normal distribution can be used (i.e., if np and nq are both greater than 5), we can calculate the probability using the normal distribution.
To perform the calculation, we need to know the mean (μ = np) and standard deviation (σ = √npq) of the distribution. The value of q is simply 1-p. We then convert the binomial problem into a normal distribution problem and use normal distribution tables or software to find the cumulative probability up to x-0.5 (because we want p(x≥9)).
For scenarios where p is very small and n is very large, the Poisson distribution may be used as an approximation for the binomial distribution.