Question

The average THC content of marijuana sold on the street is 10.4%. 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,

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 9.5.

c. Find the 73rd percentile for this distribution. %

Answer 1

X - THC content for a randomly selected bag of marijuana that is sold on the street.
a)

Mean is 0.104 , and standard deviation = 0.02


b)
9.5% = 0.095
P(X > 0.095) , Converting to standard normal

P(X > 0.095) = P( Z > -0.45) = 1 - P(Z <= -0.45) , Using standard normal table
P(Z <= -0.45) = 0.3264
P(X > 0.095) = 1 - 0.3264 = 0.6736

c)
73rd percentile. Using standard normal table, we find that probability closes to 0.73 is 0.7291 with a corresponding z-value of 0.61


X = 11.62% THC content is the 73rd percentile.