Final answer:
The distribution of X is uniformly distributed from 0 to 12. The distribution of I for a sample of 35 people is not provided. To find the probability of the average birth month being less than 7.7 for 35 people, we can use the Central Limit Theorem.
Step-by-step explanation:
The distribution of X, the number of months after January 1 that someone is born, is uniformly distributed from 0 to 12. This means that each month has an equal chance of being the birth month. The distribution can be represented as X ~ U(0, 12), where U represents the uniform distribution.
For a sample of 35 people, the distribution of I is not specified in the question. This information is missing.
To find the probability that the average birth month of the 35 people will be less than 7.7, we can use the Central Limit Theorem. Since the sample size is large (n > 30), the sample means are approximately normally distributed. We can use the mean of the population distribution (6) and the standard deviation of the population distribution (2.45) to calculate the z-score and find the probability using a standard normal distribution table or calculator.