The average THC content of marijuana sold on the street is 10%. Suppose the THC content is normally distributed with standard deviation of 2%. Let X be the THC content for a randomly selected bag of marijuana that is sold on the street. Round all answers to 4 decimal places where possible, a. What is the distribution of X? X - N( b. Find the probability that a randomly selected bag of marijuana sold on the street will have a THC content greater than 9.4. c. Find the 75th percentile for this distribution. %

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### Understanding THC Content Distribution in Marijuana

The problem involves understanding the distribution and properties of THC content in marijuana sold on the street.

#### Key Information:
- **Average THC Content:** 10%
- **Standard Deviation:** 2%
- **Distribution Type:** Normal

Let \( X \) represent the THC content of a randomly selected bag of marijuana.

### Questions:

#### a. Distribution of X

- **What is the distribution of \( X \)?**
  \[
  X \sim N(\mu, \sigma^2)
  \]
  Where \(\mu\) is the mean and \(\sigma^2\) is the variance.

#### b. Probability of THC Content Greater than 9.4%

- **How to find this probability:**
  - Calculate the probability that a randomly selected bag of marijuana has a THC content greater than 9.4%.

#### c. 75th Percentile for this Distribution

- **Finding the 75th percentile:**
  - Identify the THC content value below which 75% of the observations fall. 

All answers should be rounded to four decimal places where possible. 

This exercise helps in applying concepts of normal distribution, probability calculations, and understanding percentiles in a real-world context.
Transcribed Image Text:### Understanding THC Content Distribution in Marijuana The problem involves understanding the distribution and properties of THC content in marijuana sold on the street. #### Key Information: - **Average THC Content:** 10% - **Standard Deviation:** 2% - **Distribution Type:** Normal Let \( X \) represent the THC content of a randomly selected bag of marijuana. ### Questions: #### a. Distribution of X - **What is the distribution of \( X \)?** \[ X \sim N(\mu, \sigma^2) \] Where \(\mu\) is the mean and \(\sigma^2\) is the variance. #### b. Probability of THC Content Greater than 9.4% - **How to find this probability:** - Calculate the probability that a randomly selected bag of marijuana has a THC content greater than 9.4%. #### c. 75th Percentile for this Distribution - **Finding the 75th percentile:** - Identify the THC content value below which 75% of the observations fall. All answers should be rounded to four decimal places where possible. This exercise helps in applying concepts of normal distribution, probability calculations, and understanding percentiles in a real-world context.
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Step 1: Determine the given information

The distribution of THC content is normal. The mean is 10% and the standard deviation is 2%.

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