Answered: The average THC content of marijuana…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

The average THC content of marijuana sold on the street is 9.4%. 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, PLEASE ROUND TO 4 DECIMAL PLACES!!!!

b. Find the probability that a randomly selected bag of marijuana sold on the street will have a THC content greater than 9.9.

c. Find the 64th percentile for this distribution. %

Expert Solution

Step 1

Given:

$\begin{array}{rcl} μ & = & 9.4 \\ σ & = & 2 \end{array}$

b) The probability that a randomly selected bag of marijuana sold on the street will have a THC content greater than 9.9 is obtained as below:

$\begin{array}{rcl} P (X > 9.9) & = & 1 - P (X < 9.9) \\ = & 1 - P (\frac{X - μ}{σ} < \frac{9.9 - 9.4}{2}) \\ = & 1 - P (Z < 0.25) \end{array}$

The p-value is obtained from Excel using "NORMSDIST(z)".

Output obtained using Excel is given below:

From the output, P(z<0.25) is 0.5987.

$\begin{array}{rcl} P (X > 9.9) & = & 1 - 0.5987 \\ = & 0.4013 \end{array}$

Thus, the probability that a randomly selected bag of marijuana sold on the street will have a THC content greater than 9.9 is 0.4013.

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