Question

1) In some country, the health agency declared that the rate of catching a virus is 4 persons per day. Assuming that this rate remains constant over time, answer the following:

1. Write the probability density function that describes the probability of number of people catching the virus per day, and then calculate the probability that 45 people catch the virus per day.
2. Calculate that at least 4 people catch the virus per day.
3. Calculate the probability that 20 people catch the virus per week.
4. A hospital did a survey and in a sample of 50 people tested over 10 days and resulted in an average rate of 6 people catching the virus per day. Check that the rate given by the health agency was in fact correct or not.
5. If the health agency made a thorough investigation and found that the true rate was in fact 5.5 persons per day, what is probability that your decision in part D was in fact wrong. How powerful was your test?

2) A web-based algorithm classifies emails as spams or no-spam at a success rate of 70% of detecting a spam.

1. Find a 95% confidence interval for the number of spam emails expected within a sample of 100 emails.
2. Find a 95% confidence interval for the accuracy (standard deviation) of the detected number of spams within the 100 emails.
3. Determine the probability that at least 85 emails out of 100 emails are spams.
4. If for the 100 emails above, there was indeed actually 85 spam emails, test the claim that the same algorithm can still detect at least 85 emails with a 95% confidence.

Answer 1