Question 5: A company's social media campaign aims to engage with its audience by encouraging
users to post their own content related to the company's products. It is estimated that on any given
day, there is a 30% chance that any interaction on the company's main social media platform is a
user-generated post. On a certain day, the company monitors 15 interactions.
1. Give the distribution of Z.
Means: $Z \sim \text{Binomial}(n = 15, p = 0.3)$
2. How many of the 15 interactions do we expect NOT to be user-generated posts?
3. Find the standard deviation of the number of user-generated posts.
By using the formula for binomial distribution, find the following probabilities:
4. Find the probability that at most 5 interactions will be user-generated posts.
5. Find the probability that more than 10 interactions will be user-generated posts.
6. What is the probability that exactly 10 interactions will not be user-generated posts? (Note:
This part may need adjustment based on the new total number of trials, as it may not be
possible depending on the context.)
7. What is the probability that at least 5 interactions will be user-generated posts?