#1 find the probability The image contains a statistical problem regarding the time it takes for a pain reliever to take effect. Here's the transcription and description suitable for an educational context:---**Problem Description:**According to a study, the time between taking a pain reliever and getting relief is normally distributed with a mean of 41 minutes and a standard deviation of 8.2 minutes. Let \( X \) be the time between taking a pain reliever and getting relief.1. **Describe the probability distribution of \( X \) and state its parameters \( \mu \) and \( \sigma \):** \( X \) is \( \mu \) = [Input box] \( \sigma \) = [Input box]2. **Find the probability that the time between taking a pain reliever and getting relief for a randomly selected patient is:** a. less than 49 minutes. [Input box] (Round the answer to 4 decimal places) b. between 39 and 40 minutes. [Input box] (Round the answer to 4 decimal places) c. more than 55 minutes. [Input box] (Round the answer to 4 decimal places)**Assistance Options:**- **Question Help:** - Video 1 - Video 2 - Written Example 1 - Message instructor - Post to forum**Action Buttons:**- Submit Question- Jump to Answer---This description introduces the context of the problem, provides guidance on filling in responses, and offers various resources for assistance.

The given mean is 41 and the standard deviation is 8.2.1.The random variable X is the time between taking a pain reliever and getting relief which follows normal distribution with a mean 41 minutes and a standard deviation of 8.2 minutes. That is, .Thus, the probability distribution of X is .2.a.The probability that the time between taking a pain reliever and getting relief for a randomly selected patient is less than 49 minutes is,By using the EXCEL, the required probability is obtained below:Thus, the probability that the time between taking a pain reliever and getting relief for a randomly selected patient is less than 49 minutes is 0.8354.b.The probability that the time between taking a pain reliever and getting relief for a randomly selected patient is between 39 and 40 minutes is,By using the EXCEL, the required probability is obtained below:Thus, the probability that the time between taking a pain reliever and getting relief for a randomly selected patient is between 39 and 40 minutes is 0.0478.c.The probability that the time between taking a pain reliever and getting relief for a randomly selected patient is more than 55 minutes is,By using the EXCEL, the required probability is obtained below:Thus, the probability that the time between taking a pain reliever and getting relief for a randomly selected patient is more than 55 minutes is 0.0439.1. The probability distribution of X is .2.a. The probability that the time between taking a pain reliever and getting relief for a randomly selected patient is less than 49 minutes is 0.8354.b. The probability that the time between taking a pain reliever and getting relief for a randomly selected patient is between 39 and 40 minutes is 0.0478.c. The probability that the time between taking a pain reliever and getting relief for a randomly selected patient is more than 55 minutes is 0.0439.