Final answer:
To find the probability that a person will wait for more than 6 minutes, calculate the z-score and use the standard normal distribution. The probability is approximately 84.13%.
Step-by-step explanation:
To find the probability that a person will wait for more than 6 minutes, we need to calculate the z-score and use the standard normal distribution. The z-score is calculated by subtracting the mean (7 minutes) from the value (6 minutes) and dividing by the standard deviation (1 minute). So, the z-score is (6 - 7) / 1 = -1.
We can then look up the cumulative probability of the z-score using a standard normal distribution table or calculator. The probability that a person will wait for more than 6 minutes is the complement of the cumulative probability up to the z-score value. In this case, it is 1 minus the cumulative probability of -1.
Using a standard normal distribution table, we can find that the cumulative probability of -1 is 0.1587. Therefore, the probability that a person will wait for more than 6 minutes is 1 - 0.1587 = 0.8413, or approximately 84.13%.