Final answer:
The probability that at least 50 people will test positive out of 1500, despite not taking drugs, can be approximated using normal distribution, with calculations involving the z-score and standard normal distribution curve.
Step-by-step explanation:
The question pertains to the application of probability and statistics principles. To calculate the probability that at least 50 people out of 1500 will test positive on a drug test that is accurate 97% of the time, we would typically use the binomial distribution formula. However, as this calculation can be complex and the numbers large, an approximation using the normal distribution might be more appropriate. For this question, you would calculate the expected number of false positives (3% of 1500) and the standard deviation of this distribution, then use the standard normal distribution to find the probability of observing at least 50 false positives. This involves finding the z-score corresponding to 50 false positives and using a z-table or computational tool to find the area under the normal distribution curve that corresponds to this z-score.