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?
To answer this question, we can use the concept of the sampling distribution of the mean. The sampling distribution of the mean helps us understand the distribution of sample means when we repeatedly take samples from a population.
In this case, we are given that the mean nicotine content of the "light" cigarettes is µ milligrams and the standard deviation is σ milligrams. We are interested in finding the probability that a randomly selected sample of n cigarettes will have a total combined nicotine content of X milligrams or more.
To find this probability, we need to calculate the z-score and then use a standard normal distribution table or calculator.
The z-score is a measure of how many standard deviations an observation or sample mean is away from the mean. It is calculated using the formula:
z = (X - µ) / (σ / sqrt(n))
where X is the value we are interested in (in this case, the total combined nicotine content), µ is the population mean, σ is the population standard deviation, and n is the sample size.
In this case, we are interested in finding the probability that the total combined nicotine content is X milligrams or more. Since we have the population mean and standard deviation, we can calculate the z-score for X.
Once we have the z-score, we can use a standard normal distribution table or calculator to find the corresponding probability.
Keep in mind that this calculation assumes that the population follows a normal distribution and that the cigarettes are randomly selected from the population.
Since the specific values of the mean, standard deviation, number of cigarettes, and desired combined nicotine content were not provided in the question, you will need to substitute these values into the formula to obtain the z-score and then use a standard normal distribution table or calculator to find the probability.