Final answer:
Without specific distribution parameters such as the population mean and standard deviation of test scores, we cannot determine the probability that the average of 36 random test scores will be less than 65.
Step-by-step explanation:
The question is asking for the probability that the average of 36 random test scores will be less than 65 (P(\(\bar{x}\)<65)). To find this probability, we should assume a normal distribution of test scores and use a z-table or a technology tool like the TI-83 or TI-84 calculator, since no specific distribution parameters were provided in the question. To provide an accurate answer, I would need additional information such as the population mean (\(\mu\)) and standard deviation (\(\sigma\)) of test scores, or I would need to know that the sample mean and standard deviation are good estimates for the population parameters.
Without this crucial information, only speculative answers can be given. The provided solution snippets mention calculating probabilities and mention values such as the area to the left of a z-score, but they do not directly give us the necessary information to answer the original question. Therefore, based on the information at hand, we cannot provide a definitive answer to the question of whether the probability that the average of 36 random test scores will be less than 65 is a) 0.5, b) 0.68, c) 0.32, or d) 0.84.