Question

Q2. A certain anti-viral drug is used to cure an infection and the recovery time being
normally distributed with a mean of 28.2 months and standard deviation of 4.2 months. 25
patients who were administered this drug were randomly selected. Now, answer the
following questions with necessary justification.
(Be careful to always first check if conditions are appropriate to answer each question.
Otherwise, do not proceed with calculation.) [2+2+2+2+2+3=13 points]
(a) Compute the mean and standard deviation of the average recovery time of the selected
patients.
(b) Compute the probability that average recovery time of selected patients is between 27
and 29 months.
(c) Compute the probability that the 5-th patient in our sample recovers within 25 months.
(d) Compute the probability that the standard deviation of recovery time of selected
patients is less than 4.5 months.
(e) Compute the probability of occurrence of (b) AND (d).
(f) Compute the probability of occurrence of (b) OR (d).

Answer 1

mean and standard deviation of the average recovery time of the selected patients are 28.2 months and 0.84 months respectively.