A tobacco company claims that the nicotine content of its "light" cigarettes has a mean of milligrams and a standard deviation of milligrams. What is the probability that randomly selected light cigarettes from this company will have a total combined nicotine content of milligrams or more, assuming the company's claims to be true?
Your numbers are missing. Once you find them:
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score.
To find the probability, we need to use the properties of a normal distribution. Since we know the mean and standard deviation of the nicotine content, we can approximate the distribution of the total combined nicotine content using the Central Limit Theorem.
First, we need to calculate the mean and standard deviation of the combined nicotine content. We know that the mean of each cigarette is μ = "mean of light cigarettes" and the standard deviation is σ = "standard deviation of light cigarettes".
Let's assume that we randomly select n cigarettes. The total combined nicotine content will be the sum of the nicotine content of each individual cigarette. Since the nicotine content of each cigarette is independent, the mean of the combined nicotine content will be μ_total = n * μ and the standard deviation will be σ_total = sqrt(n) * σ.
Next, we want to calculate the probability that the total combined nicotine content is X milligrams or more. We will calculate the z-score using the formula:
z-score = (X - μ_total) / σ_total
Once we have the z-score, we can look up the corresponding probability in the standard normal distribution table or use a statistical software to find the probability.
Note: In this case, the problem does not mention the value of X, which is the number of milligrams we want to find the probability for. Therefore, we cannot provide an exact probability without knowing the value of X. But the steps outlined above can be used to calculate the probability once we have the value of X.