Step 1 :Given the mean \(\mu = 0.952\) g, the standard deviation \(\sigma = 0.324\) g, and the value from the dataset \(X = 0.369\) g.
Step 2 :We calculate the z-score using the formula: \(Z = \frac{X - \mu}{\sigma}\).
Step 3 :Substitute the given values into the formula: \(Z = \frac{0.369 - 0.952}{0.324} = -1.798\).
Step 4 :The z-score of -1.798 represents how many standard deviations the value 0.369 g is from the mean.
Step 5 :We need to find the probability that the z-score is less than -1.798. This is equivalent to finding the area to the left of -1.798 under the standard normal curve.
Step 6 :We can look up this value in a standard normal (Z) table, or use a calculator or software that can calculate it.
Step 7 :The probability that a z-score is less than -1.798 is approximately 0.0362.
Step 8 :So, the probability of randomly selecting a cigarette with 0.369 g of nicotine or less is 0.0362, or 3.62% when expressed as a percentage.
Step 9 :\(\boxed{0.0362}\) or \(\boxed{3.62\%}\) is the final answer.