According to a study, time between taking a pain reliever and getting relief is a random variable that is normally distributed with a mean of 34 minutes and a standard deviation of 5.5 minutes. Let X be the time between taking a pain reliever and getting relief for a randomly selected patient.1. Describe the probability distribution of X and state its parameters and : X ~ Select an answer Binomial Geometric Normal ( =, = )2. Find the probability that the time between taking a pain reliever and getting relief for a randomly selected patient is

a. less than 46 minutes. (Round the answer to 4 decimal places)

b. between 39 and 45 minutes. (Round the answer to 4 decimal places)

c. more than 47 minutes. (Round the answer to 4 decimal places)

3. Find the 20-th percentile for the time between taking a pain reliever and getting relief. minutes (Round the answer to 1 decimal place)