According to a study, the time between taking a pain reliever and getting relief is normally distributed with a mean of 32 minutes and a standard deviation of 5.3 minutes. Let X\displaystyle {X} be the time between taking a pain reliever and getting relief for a randomly selected patient.
  1. Describe the probability distribution of X\displaystyle {X} and state its parameters μ\displaystyle \mu and σ\displaystyle \sigma: X\displaystyle {X}  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 29 minutes. (Round the answer to 4 decimal places)
    2. between 27 and 29 minutes. (Round the answer to 4 decimal places)
    3. more than 36 minutes. (Round the answer to 4 decimal places)

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