According to a study, the time between taking a pain reliever and getting relief is normally distributed with a mean of 48 minutes and a standard deviation of 11.8 minutes. Let X\displaystyle {X}  be the time between taking a pain reliever and getting relief.
  1. Describe the probability distribution of X\displaystyle {X}  and state its parameters μ\displaystyle \mu and σ\displaystyle \sigma: is ( μ=\displaystyle \mu= , σ=\displaystyle \sigma= )
  2. Find the probability that the time between taking a pain reliever and getting relief for a randomly selected patient is
    1. less than 37 minutes. (Round the answer to 4 decimal places)
    2. between 74 and 79 minutes. (Round the answer to 4 decimal places)
    3. more than 41 minutes. (Round the answer to 4 decimal places)

License